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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCurrentReportingStatus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Current Reporting Status</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Corporatetaxespaid_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">CorporateTaxesPaid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Corporatetaxespaid_lbl" xlink:role="http://www.xbrl.org/2003/role/label">CorporateTaxesPaid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Corporatetaxespaid_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash paid for business taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating expenses:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Expenses [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 2 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Level 2</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments and Contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_JuneTwoThousandTwentyFivePreFundedWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">June Two Thousand Twenty Five Pre Funded Warrants [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_JuneTwoThousandTwentyFivePreFundedWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">June 2025 Pre-Funded Warrants.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_JuneTwoThousandTwentyFivePreFundedWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">June 2025 Pre Funded Warrants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsassumedInReverseRecapitalizationInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsassumedInReverseRecapitalizationInPeriodWeightedAverageExercisePrice</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsassumedInReverseRecapitalizationInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsassumedInReverseRecapitalizationInPeriodWeightedAverageExercisePrice</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsassumedInReverseRecapitalizationInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assumed in reverse recapitalization (in dollars per share)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockVotingRights_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Voting Rights</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockVotingRights_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Voting rights of preferred stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Period Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Fiscal Period Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionConsiderationTransferredSharesEquityInterestIssuedAndIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset acquisition, stock issued as consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionConsiderationTransferredSharesEquityInterestIssuedAndIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition, Consideration Transferred, Shares, Equity Interest Issued and Issuable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionConsiderationTransferredSharesEquityInterestIssuedAndIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Asset acquisition, consideration transferred, shares, equity interest issued and issuable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionConsiderationTransferredSharesEquityInterestIssuedAndIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Shares issued to Erigen</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityShellCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Shell Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityShellCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Shell Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquitySharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquitySharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GranteeStatusAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Grantee Status [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GranteeStatusAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Grantee Status [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Accrued Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued other liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Loan discounts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Unamortized Discount, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Instrument, Unamortized Discount, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash and Cash Equivalents, at Carrying Value, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NotesPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Notes Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NotesPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Notes Payable, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NotesPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current loan payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ProceedsFromIssuanceOfCommonStockAndCommonStockWarrantsToRelatedPartyNetOfIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds From Issuance of Common Stock and Common Stock Warrants to Related Party Net of Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ProceedsFromIssuanceOfCommonStockAndCommonStockWarrantsToRelatedPartyNetOfIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Proceeds from issuance of common stock and common stock warrants to related party net of issuance costs.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ProceedsFromIssuanceOfCommonStockAndCommonStockWarrantsToRelatedPartyNetOfIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from issuance of common stock and common stock warrants to related party net of issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Class [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset Class [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statement [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfRedeemableConvertiblePreferredStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds Net of Issuance Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfRedeemableConvertiblePreferredStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Redeemable Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionAvailabilityRemainedUnderFundingCommitment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition Availability Remained Under Funding Commitment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionAvailabilityRemainedUnderFundingCommitment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Asset acquisition availability remained under funding commitment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionAvailabilityRemainedUnderFundingCommitment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset acquisition availability remained under funding commitment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentAssetAcquiredOtherThanThroughBusinessCombinationWrittenOff_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research and Development Asset Acquired in Transaction Other than Business Combination or Joint Venture Formation, Writeoff</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentAssetAcquiredOtherThanThroughBusinessCombinationWrittenOff_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Acquired in-process research and development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, purchase price of common stock, percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Purchase Price of Common Stock, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statement [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WarrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Warrant [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WarrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Warrant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFilerCategory_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Filer Category</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFilerCategory_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Filer Category</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities and stockholders&#8217; equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Instrument [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Current Maturities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Long-Term Debt, Current Maturities, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current loan payable (net of discount and issuance costs of $38 and $74, respectively)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercisable, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Exercisable, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Lived Tangible Asset [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-Lived Tangible Asset [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SeveranceCosts1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Severance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SeveranceCosts1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash expenditures related to one-time severance payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SeveranceCosts1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Severance payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalents, Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssuedPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares Issued, Price Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssuedPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock price per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash paid for income taxes</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_SegmentGeographicalDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Geographical [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_SegmentGeographicalDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statement Geographical Axis [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonStockWarrantsToRelatedPartiesIssuanceCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock Warrants to Related Parties Issuance Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonStockWarrantsToRelatedPartiesIssuanceCost_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common Stock Warrants to Related Parties Issuance Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonStockWarrantsToRelatedPartiesIssuanceCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock Warrants to Related Parties Issuance Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionSharePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition, Share Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionSharePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Asset acquisition, share price.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionSharePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Closing price of common stock on the acquisition date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionSharePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Asset acquisition, stock price per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardPeriodOfAutomaticIncreaseToOutstandingStockMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, period of automatic increase to outstanding stock maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardPeriodOfAutomaticIncreaseToOutstandingStockMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share-based Compensation Arrangement by Share-based Payment Award, Period of Automatic Increase to Outstanding Stock Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardPeriodOfAutomaticIncreaseToOutstandingStockMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-based Compensation Arrangement by Share-based Payment Award, Period of Automatic Increase to Outstanding Stock Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Significant Accounting Policies [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Significant Accounting Policies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property, Plant and Equipment [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TrancheCTermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Tranche C Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TrancheCTermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tranch C Term Loan Member</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TrancheCTermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tranche C Term Loan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TrancheCTermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tranche C term loan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_LetterAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Letter Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_LetterAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Letter Agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_LetterAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Letter Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Granted (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Basis in Diluted Net Loss Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Earnings Per Share, Basic, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss per share attributable to common stockholders - basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net loss per share of common stock and pre-funded warrants, basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NoncashInterestAndOtherExpenseNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-cash interest and other expense, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NoncashInterestAndOtherExpenseNet_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Noncash interest and other expense, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NoncashInterestAndOtherExpenseNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncash interest and other expense, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AnnArborMichiganMemberMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Ann Arbor Michigan Member</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AnnArborMichiganMemberMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Ann Arbor Michigan Member [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AnnArborMichiganMemberMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Ann Arbor, Michigan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retirement Benefits [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Retirement Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Outstanding at end (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Outstanding at beginning (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Adjustments to reconcile net loss to net cash used in operating activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsPayableDateOfRecordDayMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Dividend record date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsPayableDateOfRecordDayMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Dividends Payable, Date of Record</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesAConvertiblePreferredStockMemberMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Series A Convertible Preferred Stock Member</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesAConvertiblePreferredStockMemberMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series A Convertible Preferred Stock Member [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesAConvertiblePreferredStockMemberMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series A</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_LitigationExpenseAmountCoveredByInsurance_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Litigation Expense Amount Covered By Insurance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_LitigationExpenseAmountCoveredByInsurance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Litigation Expense Amount Covered By Insurance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_LitigationExpenseAmountCoveredByInsurance_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amount covered by insurance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_DebtInstrumentNumberOfTranches_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt Instrument, Number of Tranches</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_DebtInstrumentNumberOfTranches_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Number of Tranches</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_DebtInstrumentNumberOfTranches_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of tranches</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Payments of debt issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments of Debt Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Payments of Debt Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Retained Earnings (Accumulated Deficit), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings (Accumulated Deficit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated deficit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ErigenAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Erigen Assets [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ErigenAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Erigen assets.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ErigenAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Erigen Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Forfeitures in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Cancelled and forfeited (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock price (in dollars per share)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock, Price Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PrepaidResearchAndDevelopmentCostsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Prepaid Research and Development Costs, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PrepaidResearchAndDevelopmentCostsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Research and Development Costs, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PrepaidResearchAndDevelopmentCostsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid research and development costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionTransactionCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset acquisition transaction costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionTransactionCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition Transaction Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionTransactionCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Asset acquisition transaction costs.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionTransactionCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Transaction costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LossContingenciesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loss Contingencies [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LossContingenciesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loss Contingencies [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Warrants issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Warrant or Right, Number of Securities Called by Warrants or Rights</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressPostalZipCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Postal Zip Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressPostalZipCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, Postal Zip Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash used in operating activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Operating Lease Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, CODM, Profit (Loss) Measure, How Used, Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IssuanceOfCommonStockToRelatedPartiesForCash_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock to related parties for cash (net of issuance costs)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IssuanceOfCommonStockToRelatedPartiesForCash_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Issuance of Common Stock to Related Parties For Cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IssuanceOfCommonStockToRelatedPartiesForCash_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Issuance of common stock to related parties for cash.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DefinedContributionPlanEmployerDiscretionaryContributionAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Defined Contribution Plan, Employer Discretionary Contribution Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DefinedContributionPlanEmployerDiscretionaryContributionAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Defined contribution plan, employer discretionary contribution amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Grants in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Granted (in dollars per share)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year Three</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2029</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Less accumulated depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionConsiderationTransferredFairValueOfSharedIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition, Consideration Transferred Fair Value Of Shared Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionConsiderationTransferredFairValueOfSharedIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Asset acquisition, consideration transferred fair value of shared issued.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionConsiderationTransferredFairValueOfSharedIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair value of shared issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Share-Based Payment Award, Stock Options, Valuation Assumptions [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Hierarchy and NAV [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Supplemental Cash Flow Information [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Supplemental disclosure of cash flow information:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Right-of-Use Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease right-of-use assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Warrant or Right [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Vested and Expected to Vest, Outstanding [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Information About Stock Options Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TypeOfArrangementAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement and Arrangement Other than Collaborative [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement and Arrangement Other than Collaborative [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Excluding Exchange Rate Effect, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net decrease in cash, cash equivalents and restricted cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAdjustmentOfWarrants_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair value of warrants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAdjustmentOfWarrants_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Adjustment of Warrants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Antidilutive securities excluded from computation of earnings</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalShareBasedCompensationStockOptionsRequisiteServicePeriodRecognition_lbl" xlink:role="http://www.xbrl.org/2003/role/label">APIC, Share-Based Payment Arrangement, Option, Increase for Cost Recognition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalShareBasedCompensationStockOptionsRequisiteServicePeriodRecognition_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, par value (in dollars per share)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfWarrants_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Warrants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfWarrants_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from the issuance of common stock, pre-funded warrants and common stock warrants, net of issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringAndRelatedActivitiesInitiationDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring and Related Activities, Initiation Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringAndRelatedActivitiesInitiationDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restructuring activities, plan adopted date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRateMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Volatility Rate, Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRateMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expected volatility, maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionContingentConsiderationLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition, Contingent Consideration, Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionContingentConsiderationLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Asset Acquisition, Contingent Consideration, Liability, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionContingentConsiderationLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset aquisition expensed</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NetProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net proceeds from sales of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NetProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Net proceeds from issuance of common stock.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NetProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Proceeds From Issuance Of Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringAndRelatedActivitiesCompletionDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring and Related Activities, Completion Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringAndRelatedActivitiesCompletionDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Effective date of workforce reduction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercise of stock options (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Exercised (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RestructuringAndRelatedCostNumberOfFullTimeEmployees_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring And Related Cost Number Of Full Time Employees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RestructuringAndRelatedCostNumberOfFullTimeEmployees_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Restructuring and related cost number of full time employees.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RestructuringAndRelatedCostNumberOfFullTimeEmployees_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of full time employees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ScheduleOfPrepaidExpensesAndOtherCurrentAssetTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Prepaid Expenses and Other Current Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ScheduleOfPrepaidExpensesAndOtherCurrentAssetTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule Of Prepaid Expenses And Other Current Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ScheduleOfPrepaidExpensesAndOtherCurrentAssetTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Prepaid Expenses And Other Current Asset [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Long-Term Debt Instruments [Table]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationVolatilityWeightingPeerHistoricalRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Volatility Weighting Peer Historical Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationVolatilityWeightingPeerHistoricalRate_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share Based Compensation Volatility Weighting Peer Historical Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationVolatilityWeightingPeerHistoricalRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Industry peers volatility rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentQuarterlyReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Quarterly Report</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByBalanceSheetGroupingTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value, by Balance Sheet Grouping [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AmendedAndRestatedTwoThousandTwentyThreeEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amended and restated two thousand twenty three equity incentive plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AmendedAndRestatedTwoThousandTwentyThreeEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amended and Restated Two Thousand Twenty Three Equity Incentive Plan [Member]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Preferred Stock, Shares Outstanding, Beginning Balance</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Warrant or Right [Domain]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_StatementGeographicalAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statement Geographical Axis [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonStockWarrantDividend_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common stock warrant dividend</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonStockWarrantDividend_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common stock warrant dividend.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Event</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_JefferiesLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Jefferies LLC</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_JefferiesLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Jefferies LLC [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_JefferiesLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Jefferies LLC</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LitigationReserveCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Estimated Litigation Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LitigationReserveCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued legal settlement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, number of additional shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Additional Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Other noncurrent assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other non-current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Antidilutive Securities [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Interest expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Interest Expense, Debt, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Expense, Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest expense, debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfCompensationCostForShareBasedPaymentArrangementsAllocationOfShareBasedCompensationCostsByPlanTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Cost by Plan [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfCompensationCostForShareBasedPaymentArrangementsAllocationOfShareBasedCompensationCostsByPlanTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Stock Based Compensation Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">AOCI Attributable to Parent [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Other Comprehensive Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionContingentConsiderationTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Total Cost of Asset Acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionContingentConsiderationTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition, Contingent Consideration [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NoncashLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-cash lease expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NoncashLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Noncash lease expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NoncashLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncash lease expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityPreferredCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redeemable Noncontrolling Interest, Equity, Preferred, Carrying Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityPreferredCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net Carrying Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDebtExtinguishmentCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepayment amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDebtExtinguishmentCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payment for Debt Extinguishment or Debt Prepayment Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loan mature date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Maturity Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Minimum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Minimum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current assets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesAWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series A Warrants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesAWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series A Warrants [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesAWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Series a warrants.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 3 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Level 3</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AtTheMarketProgramMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">At-The-Market Program</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AtTheMarketProgramMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">At-The-Market Program [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AtTheMarketProgramMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">At-The-Market Program</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TrancheATermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Tranche A Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TrancheATermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tranch A Term Loan Member</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TrancheATermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tranche A Term Loan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TrancheATermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tranche A term loan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesBConvertiblePreferredStockMemberMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Series B Convertible Preferred Stock Member</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesBConvertiblePreferredStockMemberMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series B Convertible Preferred Stock Member [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesBConvertiblePreferredStockMemberMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series B</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transactions [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending balance (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning balance (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Pre-FundedWarrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Pre-Funded Warrant [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Pre-FundedWarrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Pre-Funded Warrant [Member].</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Pre-FundedWarrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pre-Funded Warrant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromStockPlans_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Stock Plans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromStockPlans_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from the issuance of common stock under equity plan awards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesAJuniorParticipatingPreferredPurchaseRightsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Series a junior participating preferred purchase rights.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesAJuniorParticipatingPreferredPurchaseRightsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series A Junior Participating Preferred Purchase Rights [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesAJuniorParticipatingPreferredPurchaseRightsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series A Junior Participating Preferred Purchase Rights</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments and contingencies (Note 5)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-Based Compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shareholders' Equity and Share-Based Payments [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">General and Administrative Expense [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">General and Administrative Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Present value of operating lease obligations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Present value of operating lease obligations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate success bonuses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Compensation Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Deferred Compensation Liability, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Debt instrument, basis spread on variable rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Basis Spread on Variable Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Instrument, Basis Spread on Variable Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityReverseStockSplit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reverse stock split</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityReverseStockSplit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stockholders' Equity, Reverse Stock Split</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedCashCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restricted Cash, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedCashCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Insurance recovery of legal settlement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PurchaseAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchase Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PurchaseAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Purchase Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PurchaseAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Purchase Agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_LitigationSettlement_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Legal settlement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_LitigationSettlement_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Litigation Settlement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_LitigationSettlement_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Litigation settlement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongtermDebtTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongtermDebtTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term Debt, Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LossContingenciesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loss Contingencies [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LossContingenciesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loss Contingencies [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average shares used in computing basic net loss per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted-average shares used in computing basic net loss per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Weighted-average shares of common stock and pre-funded warrants outstanding, basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentInformationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Information [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentInformationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Information [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercisable, Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Exercisable, Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingExpenseInformationUsedByCodmDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, Expense Information Used by CODM, Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Share-based Compensation Arrangements by Share-based Payment Award [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionEffectiveDateOfAcquisition_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset acquisition, effective date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionEffectiveDateOfAcquisition_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition, Effective Date of Acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Lived Tangible Asset [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-Lived Tangible Asset [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TrancheBTermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Tranche B Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TrancheBTermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tranch B Term Loan Member</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TrancheBTermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tranche B Term Loan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TrancheBTermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tranche B term loan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Events [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Events</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetPurchaseAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Purchase Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetPurchaseAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Asset purchase agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetPurchaseAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset Purchase Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_O2026Q4DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">O 2026 Q4 Dividends [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_O2026Q4DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">O 2026 Q4 dividends.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_O2026Q4DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">O 2026 Q4 Dividends</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Long-Term Debt, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transactions Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related Party Transactions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesBOneConvertiblePreferredStockMemberMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Series B One Convertible Preferred Stock Member</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesBOneConvertiblePreferredStockMemberMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series B One Convertible Preferred Stock Member [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesBOneConvertiblePreferredStockMemberMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series B-1</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateTerms_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument interest term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateTerms_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Interest Rate Terms</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonStockWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock warrants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonStockWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock Warrants [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonStockWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common stock warrants.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ReversalOfFactorDeposit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Reversal Of Factor Deposit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ReversalOfFactorDeposit_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Reversal of factor deposit.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ReversalOfFactorDeposit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reversal of factor deposit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Stockholders' Equity Attributable to Parent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Convertible preferred stock, par value (in dollars per share)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Preferred stock, par or stated value per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Basis of Accounting, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Basis of Presentation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_FactorDepositPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Factor deposit paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_FactorDepositPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Factor Deposit Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_FactorDepositPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Factor deposit paid.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Stockholders' Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_FactorServicesAmountsIncurredOrPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Factor Services Amounts Incurred or Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_FactorServicesAmountsIncurredOrPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Factor services amounts incurred or payable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_FactorServicesAmountsIncurredOrPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Factor services amounts incurred or payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SeriesAPreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series A Preferred Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SeriesAPreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series A Participating Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UseOfEstimates_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Use of Estimates, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UseOfEstimates_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Use of Estimates</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseholdImprovementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Leasehold Improvements [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseholdImprovementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Leasehold improvements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine2_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Address Line Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Disclosures [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Measurements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionSharesEquityInterestYetToBeIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset acquisition, stock to be issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionSharesEquityInterestYetToBeIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition Shares Equity Interest Yet To Be Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionSharesEquityInterestYetToBeIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Asset acquisition shares equity interest yet to be issued.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Accrued Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Accrued Liabilities [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, CODM, Individual Title and Position or Group Name [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InProcessResearchAndDevelopmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">In Process Research and Development [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InProcessResearchAndDevelopmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">In Process Research and Development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Plan Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Plan Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAcceleratedVestingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Accelerated Vesting, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAcceleratedVestingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accelarated vesting of stock options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Facility [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Credit Facility [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Exercisable, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Vested and Expected to Vest, Exercisable, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesCommonStockSubjectToRepurchaseOrCancellation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares, Common Stock Subject to Repurchase or Cancellation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesCommonStockSubjectToRepurchaseOrCancellation_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Less: Weighted-average unvested restricted shares and shares subject to repurchase</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AreaOfRealEstateProperty_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Area of Real Estate Property</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AreaOfRealEstateProperty_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Area of property (in sqft)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, City or Town</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, City or Town</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Reportable Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of reportable segment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Facility [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Credit Facility [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Property, Plant and Equipment, Gross, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Property, Plant and Equipment, Gross, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Property, Plant and Equipment, Gross, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_CounterpartyNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Counterparty Name [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_CounterpartyNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Counterparty Name [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ExerciseOfPreFundedWarrants_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercise of pre-funded warrants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ExerciseOfPreFundedWarrants_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Exercise Of Pre-funded Warrants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ExerciseOfPreFundedWarrants_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Exercise of pre-funded warrants.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsCurrentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net of discount and issuance costs, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsCurrentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Issuance Costs, Current, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsCurrentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Issuance Costs, Current, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities, Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Antidilutive Securities, Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedPaymentArrangementEmployeeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Employee [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedPaymentArrangementEmployeeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Payment Arrangement, Employee</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Cash, cash equivalents and restricted cash at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Cash, cash equivalents and restricted cash at beginning of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash paid for interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statistical Measurement [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Warrant or Right, Exercise Price of Warrants or Rights</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercise price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncashOrPartNoncashAcquisitionFixedAssetsAcquired1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncash or Part Noncash Acquisition, Fixed Assets Acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncashOrPartNoncashAcquisitionFixedAssetsAcquired1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment in accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsWeightedAverageVolatilityRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Weighted Average Volatility Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsWeightedAverageVolatilityRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted Average Volatility Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_TitleOfIndividualAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Title of Individual [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_TitleOfIndividualAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title and Position [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Hierarchy and NAV [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RemainedAvailableForIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Remained available for issuance of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RemainedAvailableForIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Remained available for issuance of cmmon stock.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RemainedAvailableForIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Remained Available for issuance of Common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercisable, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Exercisable, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfFinancialPositionAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ProceedsFromIssuanceOfCommonStockPreFundedWarrantsAndCommonStockWarrantsNetOfIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds From Issuance Of Common Stock Pre Funded Warrants and Common Stock Warrants Net of Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ProceedsFromIssuanceOfCommonStockPreFundedWarrantsAndCommonStockWarrantsNetOfIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Proceeds from issuance of common stock pre funded warrants and common stock warrants net of issuance costs.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ProceedsFromIssuanceOfCommonStockPreFundedWarrantsAndCommonStockWarrantsNetOfIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from issuance of common stock, pre-funded warrants and common stock warrants, net of issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementClassOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementClassOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InProcessResearchAndDevelopmentPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/label">In Process Research and Development, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InProcessResearchAndDevelopmentPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Acquired In-Process Research and Development Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2028</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IssuanceOfPre-FundedWarrantValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Issuance Of Pre-Funded Warrant Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IssuanceOfPre-FundedWarrantValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Issuance of pre-funded warrant value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IssuanceOfPre-FundedWarrantValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of pre-funded warrants, (net of issuance costs)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumNumberOfSharesAvailableForGrantPerYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, maximum number of shares available for grant per year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumNumberOfSharesAvailableForGrantPerYear_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share-based Compensation Arrangement by Share-based Payment Award, Maximum Number of Shares Available for Grant Per Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumNumberOfSharesAvailableForGrantPerYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-based Compensation Arrangement by Share-based Payment Award, Maximum Number of Shares Available for Grant Per Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Indefinite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average shares used in computing diluted net loss per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Weighted-average shares of common stock and pre-funded warrants outstanding, diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFileNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity File Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFileNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity File Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyDepositLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Deposit Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyDepositLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Factor Invested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CoverAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cover [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRateMinimum_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Volatility Rate, Minimum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRateMinimum_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expected volatility, Minimum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SouthSanFranciscoCaliforniaMemberMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">South San Francisco California Member</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SouthSanFranciscoCaliforniaMemberMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">South San Francisco California Member [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SouthSanFranciscoCaliforniaMemberMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">South San Francisco, California</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_WaiverOffAmountPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Waiver Off Amount Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_WaiverOffAmountPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Waiver off amount payable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_WaiverOffAmountPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Waiver off amount payable under Factor MSA</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValueAddedTaxReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Value Added Tax Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValueAddedTaxReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Refund of VAT taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expense and Other Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfOutstandingStockMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, percentage of outstanding stock maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfOutstandingStockMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Percentage of Outstanding Stock Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalBalanceSheetDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Balance Sheet Components</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ThersholdIndexRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">ThersholdIndexRate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ThersholdIndexRate_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Thershold index rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ThersholdIndexRate_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">ThersholdIndexRate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ThersholdIndexRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ThersholdIndexRate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of operating segment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Operating Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sale of Stock [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment Reporting</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">General and Administrative Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">General and Administrative Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">General and administrative</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">General and administrative expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PercentageOfBeneficialOwnershipLimitationOfClassOfWarrantExercisableOnlyForCash_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage Of Beneficial Ownership Limitation Of Class Of Warrant Exercisable Only For Cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PercentageOfBeneficialOwnershipLimitationOfClassOfWarrantExercisableOnlyForCash_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of beneficial ownership limitation of class of warrant exercisable only for cash.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PercentageOfBeneficialOwnershipLimitationOfClassOfWarrantExercisableOnlyForCash_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of beneficial ownership limitation of class of warrant exercisable only for cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, Acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock in consideration of acquisition (in Share)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityLiquidationPreference_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, Liquidation Preference</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityLiquidationPreference_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate Liquidation Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, shares issued in period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Shares Issued in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionMaximumFundingCommitment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset acquisition, maximum funding commitment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionMaximumFundingCommitment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition Maximum Funding Commitment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionMaximumFundingCommitment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Asset acquisition maximum funding commitment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_A2019EmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">2019 Employee Stock Purchase Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_A2019EmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">2019 Employee Stock Purchase Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_A2019EmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2019 Employee Stock Purchase Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Rent expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AccruedClinicalTrialLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued clinical trial liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AccruedClinicalTrialLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">AccruedClinicalTrialLiability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AccruedClinicalTrialLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">AccruedClinicalTrialLiability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Maturity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Future Minimum Rental Payments under Operating Leases with Noncancelable Terms</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, Conversion of Convertible Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of shares purchase from preferred stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, award vesting period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRateMinimum_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Risk Free Interest Rate, Minimum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRateMinimum_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Risk-free interest rate, Minimum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Depreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Depreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Depreciation, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Depreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Term of Contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Term of contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Common Stock, Shares, Outstanding, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Common Stock, Shares, Outstanding, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Current loan payable (net of discount and issuance costs of $58 and nil, respectively)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current operating lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Less: current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_BrisbaneCaliforniaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Brisbane California.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_BrisbaneCaliforniaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Brisbane, California [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_BrisbaneCaliforniaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Brisbane, California</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Dividends [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TransactionCostsIncurredAsGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Transaction costs incurred as general and administrative expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TransactionCostsIncurredAsGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Transaction costs incurred as general and administrative expense.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Transition Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Transition Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_NoTradingSymbolFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">No Trading Symbol Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_NoTradingSymbolFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">No Trading Symbol Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredBonusAndProfitSharingArrangementIndividualContractTypeOfDeferredCompensationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Bonus and Profit Sharing Arrangement, Individual Contract, Type of Deferred Compensation [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfCashFlowsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Cash Flows [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Aggregate sales price of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock for cash (net of issuance costs)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Option, Activity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Stock Options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stockholders' Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net Loss Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Temporary Equity [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComputerEquipmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Computer Equipment [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComputerEquipmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Computer equipment and software</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net Income (Loss) Attributable to Parent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_StockIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Stock Issuance Costs.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_StockIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">StockIssuanceCosts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_StockIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Dividend Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Dividends</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockSplits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, Stock Splits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockSplits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fractional shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableAggregateIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Exercisable, Aggregate Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableAggregateIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Vested and Expected to Vest, Exercisable, Aggregate Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Risk-free interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Risk Free Interest Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Prepaid Expense and Other Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Prepaid expenses and other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Repayments of Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfDebt_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Repayment of loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Repayment of debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Repayment of loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Year Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Fiscal Year Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PrivateInvestmentInPublicEntityFinancingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Private investment in public entity financing.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PrivateInvestmentInPublicEntityFinancingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Private Investment In Public Entity Financing [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PrivateInvestmentInPublicEntityFinancingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">PIPE Financing</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredBonusMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred Bonus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredBonusMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Bonus [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investing activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CompensationAndRetirementDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retirement Benefits [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accounts Payable, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedInPeriodFairValue1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested in Period, Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedInPeriodFairValue1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, fair value of stock options vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Interest expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Expense, Nonoperating</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Interest Expense, Nonoperating, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research and Development Expense [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Research and Development Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionDateOfAcquisitionAgreement_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition, Date of Acquisition Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionDateOfAcquisitionAgreement_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset acquisition, agreement date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_UnauditedInterimFinancialStatementPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Unaudited Interim Financial Statement, Policy</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_UnauditedInterimFinancialStatementPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unaudited Interim Financial Statement, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_UnauditedInterimFinancialStatementPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unaudited Interim Financial Statement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Disclosures [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, Acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock in consideration of acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2027</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IndividualsWhoWereNotPreviouslyEmployeesOrDirectorsOfCompanyMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Individuals who were not previously employees or directors of company.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IndividualsWhoWereNotPreviouslyEmployeesOrDirectorsOfCompanyMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Individuals Who Were Not Previously Employees or Directors Of Company [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IndividualsWhoWereNotPreviouslyEmployeesOrDirectorsOfCompanyMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Individuals who were not Previously Employees or Directors of Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockConsiderationReceivedOnTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock, Consideration Received on Transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockConsiderationReceivedOnTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Consideration received</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_BrisbaneCaliforniaAndAnnArborMichiganMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Brisbane, California and Ann Arbor Michigan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_BrisbaneCaliforniaAndAnnArborMichiganMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Brisbane California and Ann Arbor Michigan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_BrisbaneCaliforniaAndAnnArborMichiganMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Brisbane, California and Ann Arbor Michigan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RightsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Rights Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RightsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Rights [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionConsiderationTransferredEquityInterestIssuedAndIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition, Consideration Transferred, Equity Interest Issued and Issuable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionConsiderationTransferredEquityInterestIssuedAndIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset acquisition, equity issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sale of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_DebtInstrumentExitFee_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument Exit Fee</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_DebtInstrumentExitFee_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt instrument exit fee.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_DebtInstrumentExitFee_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument, exit fee</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityLiquidationPreferencePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Per Share Liquidation Preference</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityLiquidationPreferencePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, Liquidation Preference Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash used in investing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrivatePlacementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Private Placement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrivatePlacementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Private Placement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Warrants [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common warrants.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Warrants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12bTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title of 12(b) Security</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12bTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Title of 12(b) Security</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Forfeitures in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cancelled and forfeited (in dollars per share)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquitySharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquitySharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, Shares Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SouthSanFranciscoCaliforniaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">South San Francisco, California.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SouthSanFranciscoCaliforniaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">South San Francisco, California [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SouthSanFranciscoCaliforniaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">South San Francisco, California</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesIssuedBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Issued, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesIssuedBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average common shares outstanding (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesIssuedBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Weighted-average common shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Remainder of Fiscal Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2026 (excluding three months ended March 31, 2026)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentInformationTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Information [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentInformationTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Information [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Changes in operating assets and liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Property and Equipment, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Outstanding at end (in dollars per share)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Outstanding at beginning (in dollars per share)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Outstanding (in dollars per share)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AcquiredIn-ProcessResearchAndDevelopment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Acquired in-process research and development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AcquiredIn-ProcessResearchAndDevelopment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Acquired In - Process Research And Development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AcquiredIn-ProcessResearchAndDevelopment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Acquired in - process research and development.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InsuranceSettlementsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Insurance Settlements Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InsuranceSettlementsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Insurance settlements receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Text Block]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional Paid-In Capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid-in Capital [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accrued Liabilities and Other Operating Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued expenses and other liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementFrequencyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Frequency [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementFrequencyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Measurement Frequency [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementLocationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Income Location, Balance [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementLocationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Statement Location [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Trading Symbol</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trading Symbol</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRateMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Risk-free interest rate, Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRateMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Risk Free Interest Rate, Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingPeriodIncreaseDecrease_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Period Increase (Decrease)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingPeriodIncreaseDecrease_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Period Increase (Decrease), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingPeriodIncreaseDecrease_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share based compensation, modified stock options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PercentageOfCommissionOnSaleOfStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of commission on sale of stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PercentageOfCommissionOnSaleOfStock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of commission on sale of stock.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PercentageOfCommissionOnSaleOfStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage Of Commission On Sale Of Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Employee-related Liabilities, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee-related Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Financing activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expected term (in years)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsRecurringMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Recurring [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsRecurringMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value, Recurring</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total minimum lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PreFundedWarrantAndCommonWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Pre Funded Warrant And Common Warrants [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PreFundedWarrantAndCommonWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Pre funded&#160;warrant and common warrants.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PreFundedWarrantAndCommonWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pre Funded Warrant And Common Warrants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Less: imputed interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Ecor1CapitalLlcAndVersantVentureCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">EcoR1 Capital, LLC and Versant Venture Capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Ecor1CapitalLlcAndVersantVentureCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">EcoR1 Capital LLC and Versant Venture Capital.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Ecor1CapitalLlcAndVersantVentureCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">EcoR1 Capital LLC And Versant Venture Capital [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Components [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity Components [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageRemainingContractualTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Exercisable, Weighted Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageRemainingContractualTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Vested and Expected to Vest, Exercisable, Weighted Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpenseExcludingAcquiredInProcessCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research and Development Expense (Excluding Acquired in Process Cost)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpenseExcludingAcquiredInProcessCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Research and development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationArrangementWithIndividualAllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Compensation Arrangement with Individual, Allocated Share-Based Compensation Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationArrangementWithIndividualAllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock compensation expense related to employees stock options grants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total other income (expense), net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Total other income (expenses), net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Nonoperating Income (Expense)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityComponentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Component [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityComponentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity Component [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByAssetClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Class [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByAssetClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset Class [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PublicFloat_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Public Float</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PublicFloat_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Public float.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PublicFloat_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Public float</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, expiration period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Expiration Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockVotingRights_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Voting Rights</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockVotingRights_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Voting rights of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Pre-FundedWarrantsIssuanceCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pre-funded warrants issuance cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Pre-FundedWarrantsIssuanceCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Pre-Funded Warrants Issuance Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Pre-FundedWarrantsIssuanceCost_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Pre-funded warrants issuance cost.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Maximum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalCashFlowElementsInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Cash Flow Elements, Investing Activity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalCashFlowElementsInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-cash investing activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IssuanceOfCommonStockValueUnderEquityPlanAwards_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Issuance of common stock value under equity plan awards.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IssuanceOfCommonStockValueUnderEquityPlanAwards_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Issuance Of Common Stock Value Under Equity Plan Awards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IssuanceOfCommonStockValueUnderEquityPlanAwards_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock under equity plan awards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statistical Measurement [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Exercises in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercised (in dollars per share)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Prepaid Expense, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expense, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Value, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, $0.001 par value; 100,000,000 shares authorized; 14,344,034 and 4,927,161 shares issued and outstanding at March 31, 2026 and December 31, 2025, respectively</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationArrangementWithIndividualExcludingShareBasedPaymentsAndPostretirementBenefitsByTypeOfDeferredCompensationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Bonus and Profit Sharing Arrangements, Individual Contracts, Type of Deferred Compensation [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Dividends [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total stockholders&#8217; equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ProceedsFromIssuanceOfCommonStockWarrants_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds From Issuance Of Common Stock Warrants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ProceedsFromIssuanceOfCommonStockWarrants_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Proceeds from issuance of common stock warrants.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ProceedsFromIssuanceOfCommonStockWarrants_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from the issuance of common stock and common stock warrants to related party, net of issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAssumedInReverseRecapitalizationInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAssumedInReverseRecapitalizationInPeriod</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAssumedInReverseRecapitalizationInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAssumedInReverseRecapitalizationInPeriod</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAssumedInReverseRecapitalizationInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assumed in reverse recapitalization (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquipmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equipment [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquipmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lab equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_OperatingLeaseCommencementMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease Commencement Month And Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_OperatingLeaseCommencementMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Operating lease commencement month and year.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_OperatingLeaseCommencementMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease commencement month and year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpenseAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other income (expense), net:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpenseAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Nonoperating Income (Expense) [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Volatility Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expected volatility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RoyaltyExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Royalty payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RoyaltyExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Royalty Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loan Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentPeriodicPaymentPrincipal_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Monthly principal payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentPeriodicPaymentPrincipal_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Periodic Payment, Principal</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentPeriodicPaymentPrincipal_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Instrument, Periodic Payment, Principal</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireInProcessResearchAndDevelopment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire in Process Research and Development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireInProcessResearchAndDevelopment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expensed as acquired in-process research and development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest income and other income (expense), net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Nonoperating Income (Expense)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Nonoperating Income (Expense), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Additional Paid in Capital, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid in Capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional paid-in capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Events [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income Tax Expense (Benefit), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Expense (Benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Provision for income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByMeasurementFrequencyAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Frequency [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByMeasurementFrequencyAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Measurement Frequency [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Gross proceeds from issuance of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from the issuance of common stock, net of issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TwoThousandTwentyThreeInducementPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2023 Inducement Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TwoThousandTwentyThreeInducementPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand twenty three inducement plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TwoThousandTwentyThreeInducementPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty Three Inducement Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonStockToRelatedPartiesIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock to Related Parties Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonStockToRelatedPartiesIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common stock to related parties issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonStockToRelatedPartiesIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common stock to related parties issuance costs.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Common Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Common Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseRemainingLeaseTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Remaining Lease Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseRemainingLeaseTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Remaining lease term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AmendedAndRestatedTwoThousandNineteenEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amended and Restated 2019 Equity Incentive Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AmendedAndRestatedTwoThousandNineteenEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amended and Restated Two Thousand Nineteen Equity Incentive Plan Member</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AmendedAndRestatedTwoThousandNineteenEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amended and restated two thousand nineteen equity incentive plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Payments to Acquire Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Purchase of property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityByClassOfStockTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, by Class of Stock [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityByClassOfStockTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Temporary Equity, by Class of Stock [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Term Loan Member</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Term Loan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Term loan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property, Plant and Equipment [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercisable, Weighted Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Exercisable, Weighted Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Statement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares issued in transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock, Number of Shares Issued in Transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Issuance of common stock for cash (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Issuance of common stock for cash, net of issuance cost (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock for cash (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ExerciseOfPre-FundedWarrantsShares_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercise of pre-funded warrants (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ExerciseOfPre-FundedWarrantsShares_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Exercise of pre-funded warrants Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ExerciseOfPre-FundedWarrantsShares_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Exercise of pre-funded warrants Shares.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquitySharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquitySharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Earnings Per Share, Diluted, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss per share attributable to common stockholders - diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net loss per share of common stock and pre-funded warrants, diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableTrade_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accounts Payable, Trade</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableTrade_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_TitleOfIndividualWithRelationshipToEntityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title and Position [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_TitleOfIndividualWithRelationshipToEntityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Title of Individual [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Dividends</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Dividends, Common Stock, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Dividends, Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">City Area Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">City Area Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IssuanceOfCommonStockShareToRelatedPartiesForCash_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock to related parties for cash (net of issuance costs) (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IssuanceOfCommonStockShareToRelatedPartiesForCash_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Issuance of Common Stock Share to Related Parties For Cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IssuanceOfCommonStockShareToRelatedPartiesForCash_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Issuance of common stock share to related parties for cash.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AcquiredInProcessResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Acquired in Process Research and Development Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AcquiredInProcessResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Acquired in process research and development expense.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AcquiredInProcessResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Acquired in process research and development expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Loan amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Face Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument, face amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Borrowing capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_O2023Q4DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">O 2023 Q4 Dividends [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_O2023Q4DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">O 2023 Q4 Dividends [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_O2023Q4DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">O 2023 Q4 Dividends.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Counterparty Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Counterparty Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessExitCosts1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Exit Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessExitCosts1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exit fee</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NumberOfNonCancelableOperatingLeaseAgreements_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">NumberOfNonCancelableOperatingLeaseAgreements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NumberOfNonCancelableOperatingLeaseAgreements_lbl" xlink:role="http://www.xbrl.org/2003/role/label">NumberOfNonCancelableOperatingLeaseAgreements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NumberOfNonCancelableOperatingLeaseAgreements_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of non-cancelable lease agreements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesBWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series B Warrants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesBWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series B warrants [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesBWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Series b warrants.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseExpirationDate1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expiration date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseExpirationDate1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease Expiration Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RegisteredDirectOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Registered Direct Offering</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RegisteredDirectOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Registered Direct Offering [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RegisteredDirectOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Registered Direct Offering [Member].</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RegisteredDirectOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">RDO</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LetterOfCreditMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Letter of Credit [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LetterOfCreditMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Letter of Credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtPercentageBearingVariableInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Annual floating interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtPercentageBearingVariableInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Percentage Bearing Variable Interest, Percentage Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtPercentageBearingVariableInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term Debt, Percentage Bearing Variable Interest, Percentage Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Property and equipment-net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Property and equipment-net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Exercisable, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Vested and Expected to Vest, Exercisable, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Income (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Loss from operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_O2026Q1DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">O 2026 Q1 Dividends [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_O2026Q1DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">O 2026 Q1 Dividends.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_O2026Q1DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">O 2026 Q1 Dividends</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Deficit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionConsiderationTransferred_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset acquisition, aggregate consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionConsiderationTransferred_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition, Consideration Transferred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionConsiderationTransferred_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionConsiderationTransferred_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Total consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringAndRelatedCostNumberOfPositionsEliminated_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring and Related Cost, Number of Positions Eliminated</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringAndRelatedCostNumberOfPositionsEliminated_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of employees eliminated</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease liabilities, less current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Noncurrent operating lease obligations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 1 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Level 1</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class of Stock [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash provided by (used in) financing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonStockWarrantsIssuanceCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock Warrants Issuance Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonStockWarrantsIssuanceCost_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common stock warrants issuance cost.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonStockWarrantsIssuanceCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock Warrants Issuance Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityInteractiveDataCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Interactive Data Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityInteractiveDataCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Interactive Data Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RemainingPrincipalAndAccruedInterestPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Remaining Principal And Accrued Interest Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RemainingPrincipalAndAccruedInterestPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Remaining Principal And Accrued Interest Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RemainingPrincipalAndAccruedInterestPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Remaining principal and accrued interest payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementLocationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Income Location, Balance [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementLocationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Statement Location [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FurnitureAndFixturesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Furniture and Fixtures [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FurnitureAndFixturesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Furniture and fixtures</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityTaxIdentificationNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Tax Identification Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityTaxIdentificationNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Tax Identification Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stockholders' equity:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Including Portion Attributable to Noncontrolling Interest [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongtermDebtTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongtermDebtTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term Debt, Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Organization, Consolidation and Presentation of Financial Statements Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Organization and Description of the Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_LocalPhoneNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Local Phone Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_LocalPhoneNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Local Phone Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NovemberTwoThousandTwentyFivePreFundedWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">November 2025 Pre Funded Warrants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NovemberTwoThousandTwentyFivePreFundedWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">November Two Thousand Twenty Five Pre Funded Warrants [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NovemberTwoThousandTwentyFivePreFundedWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">November 2025 Pre-Funded Warrants.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based payment arrangement, nonvested award, option, cost not yet recognized, amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Nonvested Award, Option, Cost Not yet Recognized, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Diluted [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Denominator:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SouthSanFranciscoCaliforniaAndAnnArborMichiganMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">South San Francisco California and Ann Arbor Michigan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SouthSanFranciscoCaliforniaAndAnnArborMichiganMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">South San Francisco, California and Ann Arbor, Michigan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SouthSanFranciscoCaliforniaAndAnnArborMichiganMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">South San Francisco, California and Ann Arbor, Michigan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SaleOfStockWarrantsIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale Of Stock Warrants Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SaleOfStockWarrantsIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Sale of stock warrants issued.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SaleOfStockWarrantsIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of warrants issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountingPoliciesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Policies [Abstract]</link:label>
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  <xsd:element id="tpst_O2026Q1DividendsMember" name="O2026Q1DividendsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_SeriesBConvertiblePreferredStockMemberMember" name="SeriesBConvertiblePreferredStockMemberMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_RestructuringAndRelatedCostNumberOfFullTimeEmployees" name="RestructuringAndRelatedCostNumberOfFullTimeEmployees" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_AssetPurchaseAgreementMember" name="AssetPurchaseAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_PreFundedWarrantAndCommonWarrantsMember" name="PreFundedWarrantAndCommonWarrantsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsassumedInReverseRecapitalizationInPeriodWeightedAverageExercisePrice" name="ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsassumedInReverseRecapitalizationInPeriodWeightedAverageExercisePrice" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_ProceedsFromIssuanceOfCommonStockWarrants" name="ProceedsFromIssuanceOfCommonStockWarrants" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_SeriesAJuniorParticipatingPreferredPurchaseRightsMember" name="SeriesAJuniorParticipatingPreferredPurchaseRightsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_AssetAcquisitionSharesEquityInterestYetToBeIssued" name="AssetAcquisitionSharesEquityInterestYetToBeIssued" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_StockIssuanceCosts" name="StockIssuanceCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_NumberOfNonCancelableOperatingLeaseAgreements" name="NumberOfNonCancelableOperatingLeaseAgreements" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAssumedInReverseRecapitalizationInPeriod" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAssumedInReverseRecapitalizationInPeriod" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_CommonStockWarrantsIssuanceCost" name="CommonStockWarrantsIssuanceCost" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_ScheduleOfPrepaidExpensesAndOtherCurrentAssetTableTextBlock" name="ScheduleOfPrepaidExpensesAndOtherCurrentAssetTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_AnnArborMichiganMemberMember" name="AnnArborMichiganMemberMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_DebtInstrumentExitFee" name="DebtInstrumentExitFee" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_LitigationExpenseAmountCoveredByInsurance" name="LitigationExpenseAmountCoveredByInsurance" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="tpst_A2019EmployeeStockPurchasePlanMember" name="A2019EmployeeStockPurchasePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_ThersholdIndexRate" name="ThersholdIndexRate" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="tpst_NovemberTwoThousandTwentyFivePreFundedWarrantsMember" name="NovemberTwoThousandTwentyFivePreFundedWarrantsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_NoncashLeaseExpense" name="NoncashLeaseExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_PurchaseAgreementMember" name="PurchaseAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_BrisbaneCaliforniaAndAnnArborMichiganMember" name="BrisbaneCaliforniaAndAnnArborMichiganMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_WaiverOffAmountPayable" name="WaiverOffAmountPayable" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="tpst_PrepaidResearchAndDevelopmentCostsCurrent" name="PrepaidResearchAndDevelopmentCostsCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_IndividualsWhoWereNotPreviouslyEmployeesOrDirectorsOfCompanyMember" name="IndividualsWhoWereNotPreviouslyEmployeesOrDirectorsOfCompanyMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_PercentageOfCommissionOnSaleOfStock" name="PercentageOfCommissionOnSaleOfStock" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_IssuanceOfCommonStockSharesUnderEquityPlanAwards" name="IssuanceOfCommonStockSharesUnderEquityPlanAwards" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_ShareBasedCompensationVolatilityWeightingPeerHistoricalRate" name="ShareBasedCompensationVolatilityWeightingPeerHistoricalRate" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_O2023Q4DividendsMember" name="O2023Q4DividendsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_SouthSanFranciscoCaliforniaAndAnnArborMichiganMember" name="SouthSanFranciscoCaliforniaAndAnnArborMichiganMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_IssuanceOfCommonStockShareToRelatedPartiesForCash" name="IssuanceOfCommonStockShareToRelatedPartiesForCash" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_PublicFloat" name="PublicFloat" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_IssuanceOfPre-FundedWarrantValue" name="IssuanceOfPre-FundedWarrantValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_AssetAcquisitionTransactionCosts" name="AssetAcquisitionTransactionCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_OperatingLeaseCommencementMonthAndYear" name="OperatingLeaseCommencementMonthAndYear" type="xbrli:gYearMonthItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_ReversalOfFactorDeposit" name="ReversalOfFactorDeposit" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="tpst_NoncashInterestAndOtherExpenseNet" name="NoncashInterestAndOtherExpenseNet" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_AssetAcquisitionAvailabilityRemainedUnderFundingCommitment" name="AssetAcquisitionAvailabilityRemainedUnderFundingCommitment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="tpst_Pre-FundedWarrantMember" name="Pre-FundedWarrantMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_ExerciseOfPre-FundedWarrantsShares" name="ExerciseOfPre-FundedWarrantsShares" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_AccruedClinicalTrialLiability" name="AccruedClinicalTrialLiability" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="tpst_TrancheATermLoanMember" name="TrancheATermLoanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_UnauditedInterimFinancialStatementPolicyPolicyTextBlock" name="UnauditedInterimFinancialStatementPolicyPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_SeriesAConvertiblePreferredStockMemberMember" name="SeriesAConvertiblePreferredStockMemberMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_O2026Q4DividendsMember" name="O2026Q4DividendsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_SouthSanFranciscoCaliforniaMember" name="SouthSanFranciscoCaliforniaMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_PercentageOfBeneficialOwnershipLimitationOfClassOfWarrantExercisableOnlyForCash" name="PercentageOfBeneficialOwnershipLimitationOfClassOfWarrantExercisableOnlyForCash" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_CommonStockWarrantDividend" name="CommonStockWarrantDividend" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="tpst_PrivateInvestmentInPublicEntityFinancingMember" name="PrivateInvestmentInPublicEntityFinancingMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_AssetAcquisitionConsiderationTransferredSharesEquityInterestIssuedAndIssuable" name="AssetAcquisitionConsiderationTransferredSharesEquityInterestIssuedAndIssuable" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_ProceedsFromIssuanceOfCommonStockPreFundedWarrantsAndCommonStockWarrantsNetOfIssuanceCosts" name="ProceedsFromIssuanceOfCommonStockPreFundedWarrantsAndCommonStockWarrantsNetOfIssuanceCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_RemainingPrincipalAndAccruedInterestPayable" name="RemainingPrincipalAndAccruedInterestPayable" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="tpst_TransactionCostsIncurredAsGeneralAndAdministrativeExpense" name="TransactionCostsIncurredAsGeneralAndAdministrativeExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_BrisbaneCaliforniaMember" name="BrisbaneCaliforniaMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_DebtInstrumentNumberOfTranches" name="DebtInstrumentNumberOfTranches" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="tpst_SaleOfStockWarrantsIssued" name="SaleOfStockWarrantsIssued" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="tpst_JuneTwoThousandTwentyFivePreFundedWarrantsMember" name="JuneTwoThousandTwentyFivePreFundedWarrantsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardPeriodOfAutomaticIncreaseToOutstandingStockMaximum" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardPeriodOfAutomaticIncreaseToOutstandingStockMaximum" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_IssuanceOfCommonStockValueUnderEquityPlanAwards" name="IssuanceOfCommonStockValueUnderEquityPlanAwards" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="tpst_AssetAcquisitionMaximumFundingCommitment" name="AssetAcquisitionMaximumFundingCommitment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="tpst_Ecor1CapitalLlcAndVersantVentureCapitalMember" name="Ecor1CapitalLlcAndVersantVentureCapitalMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_IssuanceOfCommonStockWarrants" name="IssuanceOfCommonStockWarrants" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_RegisteredDirectOfferingMember" name="RegisteredDirectOfferingMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_Corporatetaxespaid" name="Corporatetaxespaid" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="tpst_SeriesBOneConvertiblePreferredStockMemberMember" name="SeriesBOneConvertiblePreferredStockMemberMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_TrancheCTermLoanMember" name="TrancheCTermLoanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_ExerciseOfPreFundedWarrants" name="ExerciseOfPreFundedWarrants" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="tpst_LetterAgreementMember" name="LetterAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_IssuanceOfCommonStockWarrantsToRelatedParties" name="IssuanceOfCommonStockWarrantsToRelatedParties" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="tpst_CommonStockToRelatedPartiesIssuanceCosts" name="CommonStockToRelatedPartiesIssuanceCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_ErigenAssetsMember" name="ErigenAssetsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_ProceedsFromIssuanceOfCommonStockAndCommonStockWarrantsToRelatedPartyNetOfIssuanceCosts" name="ProceedsFromIssuanceOfCommonStockAndCommonStockWarrantsToRelatedPartyNetOfIssuanceCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_SeriesAWarrantsMember" name="SeriesAWarrantsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_AssetAcquisitionConsiderationTransferredFairValueOfSharedIssued" name="AssetAcquisitionConsiderationTransferredFairValueOfSharedIssued" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_SeriesBWarrantsMember" name="SeriesBWarrantsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_JefferiesLLCMember" name="JefferiesLLCMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_AtTheMarketProgramMember" name="AtTheMarketProgramMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_LitigationSettlement" name="LitigationSettlement" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="tpst_TwoThousandTwentyThreeInducementPlanMember" name="TwoThousandTwentyThreeInducementPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_AmendedAndRestatedTwoThousandNineteenEquityIncentivePlanMember" name="AmendedAndRestatedTwoThousandNineteenEquityIncentivePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_AcquiredIn-ProcessResearchAndDevelopment" name="AcquiredIn-ProcessResearchAndDevelopment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_RemainedAvailableForIssuanceOfCommonStock" name="RemainedAvailableForIssuanceOfCommonStock" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="tpst_SouthSanFranciscoCaliforniaMemberMember" name="SouthSanFranciscoCaliforniaMemberMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_AmendedAndRestatedTwoThousandTwentyThreeEquityIncentivePlanMember" name="AmendedAndRestatedTwoThousandTwentyThreeEquityIncentivePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_TermLoanMember" name="TermLoanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_TrancheBTermLoanMember" name="TrancheBTermLoanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_CommonStockWarrantsToRelatedPartiesIssuanceCost" name="CommonStockWarrantsToRelatedPartiesIssuanceCost" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="tpst_Pre-FundedWarrantsIssuanceCost" name="Pre-FundedWarrantsIssuanceCost" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_CommonStockWarrantsMember" name="CommonStockWarrantsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_AcquiredInProcessResearchAndDevelopmentExpense" name="AcquiredInProcessResearchAndDevelopmentExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_NetProceedsFromIssuanceOfCommonStock" name="NetProceedsFromIssuanceOfCommonStock" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_AssetAcquisitionSharePrice" name="AssetAcquisitionSharePrice" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_FactorDepositPaid" name="FactorDepositPaid" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
</xsd:schema>
