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<!-- DFIN New ActiveDisclosure (SM) XBRL Linkbase Document - http://www.dfinsolutions.com/ -->
<!-- Creation Date :2023-08-10T16:35:10.9444+00:00 -->
<!-- Copyright (c) 2023 Donnelly Financial Solutions, Inc. All Rights Reserved. -->
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    <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_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>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SaleOfStockWarrantCovenantsNoticePeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Sale of stock, warrant covenants, notice 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_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>
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    <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>
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    <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="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="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_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_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_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_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="srt_TitleOfIndividualWithRelationshipToEntityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title of Individual [Domain]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalCashFlowElementsOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-cash operating activities:</link:label>
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    <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="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_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_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_OperatingLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease liabilities, less current portion</link:label>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfStockByClassTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Stock by Class [Table]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfStockByClassTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Stock by Class [Table]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SaleOfStockWarrantCovenantsMaximumOwnershipPercentageAfterIssuingNotice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Beneficial ownership percentage after issuing notice</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SaleOfStockWarrantCovenantsMaximumOwnershipPercentageAfterIssuingNotice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale Of Stock Warrant Covenants Maximum Ownership Percentage After Issuing Notice</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SaleOfStockWarrantCovenantsMaximumOwnershipPercentageAfterIssuingNotice_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Sale of stock, warrant covenants, maximum ownership percentage after issuing notice.</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_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_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current assets</link:label>
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    <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>
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    <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="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="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/terseLabel">Issuance of common stock for cash, net of issuance cost</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_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/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/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="tpst_CommonStockWarrantsMemberMember_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_CommonStockWarrantsMemberMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock Warrants Member [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonStockWarrantsMemberMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common Stock Warrants Member</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="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="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_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_PrepaidExpenseAndOtherAssetsCurrent_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_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_NetIncomeLossAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Numerator:</link:label>
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    <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_TrancheCTermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tranche C term loan.</link:label>
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    <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>
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    <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>
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    <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="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="us-gaap_ClassOfWarrantOrRightOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pre-funded warrants unexercised</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Warrant or Right, Outstanding</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_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/terseLabel">Non-cash 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/terseLabel">Ann Arbor, Michigan</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/documentation">Ann Arbor Michigan Member</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_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_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_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_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_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_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="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_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/documentation">Series A Convertible Preferred Stock Member</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="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_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="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="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="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="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_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/documentation">Litigation Expense Amount Covered By Insurance</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_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="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/documentation">Debt Instrument, Number of Tranches</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="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/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/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_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="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_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_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/totalLabel">Long-Term Debt, Total</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_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/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_ClassOfStockDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class of Stock [Domain]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfStockDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Domain]</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="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/documentation">Prepaid Research and Development Costs, Current</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="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="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pre-funded warrants exercised</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_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_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_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_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/totalLabel">Total</link:label>
    <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>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Preferred Stock, Shares Outstanding, Ending Balance</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Outstanding</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, shares outstanding</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_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="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="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="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_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">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_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_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Operating Capital [Abstract]</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="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/verboseLabel">Payments of debt issuance costs</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TwoThousandTwentyThreeEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2023 Equity Incentive Plan</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TwoThousandTwentyThreeEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty Three Equity Incentive Plan [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TwoThousandTwentyThreeEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand twenty three equity incentive plan.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Plan Name [Axis]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Plan Name [Axis]</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="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="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_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_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_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_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="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_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_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_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_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_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_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="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="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="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net of discount and issuance costs</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Issuance Costs, Net</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Issuance Costs, Net, 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/terseLabel">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/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/totalLabel">Retained Earnings (Accumulated Deficit), Total</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_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_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">Deficit Accumulated</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_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_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="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/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/periodEndLabel">Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest, Ending Balance</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="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="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_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_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_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/label">Operating Lease, Liability</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_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_EmployeeStockOptionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Options to purchase common stock</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeStockOptionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee Stock Option [Member]</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_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_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_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustments to Reconcile Net Income (Loss) to Cash Provided by (Used in) Operating Activities [Abstract]</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_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_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="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_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/verboseLabel">Debt instrument, basis spread on variable rate</link:label>
    <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="dei_EntityCurrentReportingStatus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Current Reporting Status</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="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_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="us-gaap_FairValueByBalanceSheetGroupingTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, by Balance Sheet Grouping [Table]</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_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="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_StockIssuedDuringPeriodValueConversionOfUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Conversion of preferred stock to common stock</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueConversionOfUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, Conversion of Units</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="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/terseLabel">Schedule of Prepaid Expenses and Other Current Asset</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; 12,583,833 and 10,518,539 shares issued and outstanding at Jun 30, 2023 and December 31, 2022, respectively</link:label>
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    <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_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_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_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_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_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_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="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Liabilities, Current</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>
    <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="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="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="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="tpst_AmendedAndRestatedTwoThousandTwentyThreeEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amended and Restated 2023 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>
    <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="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_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/totalLabel">Income Tax Expense (Benefit), Total</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_StockholdersEquityNoteStockSplitExchangeRatio_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">StockholdersEquityNoteStockSplitExchangeRatio</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_StockholdersEquityNoteStockSplitExchangeRatio_lbl" xlink:role="http://www.xbrl.org/2003/role/label">StockholdersEquityNoteStockSplitExchangeRatio</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_StockholdersEquityNoteStockSplitExchangeRatio_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">StockholdersEquityNoteStockSplitExchangeRatio</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_StockholdersEquityNoteStockSplitExchangeRatio_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Stock split exchange ratio</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_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_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_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_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="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_IncreaseDecreaseInOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease liabilities</link:label>
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    <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="us-gaap_TemporaryEquityLiquidationPreferencePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Per Share Liquidation Preference</link:label>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Taxes Paid</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>
    <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="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_DebtInstrumentFaceAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument, face amount</link:label>
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    <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_TemporaryEquityDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity Disclosure [Abstract]</link:label>
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    <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>
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    <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="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="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/terseLabel">Non-cash lease expense</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_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_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/verboseLabel">Other noncurrent assets</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_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_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_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_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_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_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_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_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="us-gaap_InterestPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Paid, Excluding Capitalized Interest, Operating Activities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestAndDividendsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest payable</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestAndDividendsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest and Dividends Payable, Current</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestAndDividendsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Interest and Dividends Payable, Current, Total</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="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/documentation">At-The-Market Program</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_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/totalLabel">Additional Paid in Capital, Total</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_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_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_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="us-gaap_AdditionalCashFlowElementsInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Cash Flow Elements, Investing Activities [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/documentation">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/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/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/verboseLabel">Tranche A Term Loan</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="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="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="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/documentation">Series B Convertible Preferred Stock Member</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="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_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_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_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_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_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_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_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_AccountingPoliciesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Policies [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SaleOfStockWarrantCovenantsMaximumOwnershipPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Beneficial ownership percentage</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SaleOfStockWarrantCovenantsMaximumOwnershipPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale Of Stock Warrant Covenants Maximum Ownership Percentage</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SaleOfStockWarrantCovenantsMaximumOwnershipPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Sale of stock, warrant covenants, maximum ownership percentage.</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/label">EcoR1 Capital, LLC and Versant Venture Capital [Member]</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="us-gaap_StockIssuedDuringPeriodSharesConversionOfUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, Conversion of Units</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Conversion of preferred stock to common stock (in shares)</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="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_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="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="tpst_ExerciseOfPreFundedWarrantsShares_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercise of pre funded warrants, shares</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ExerciseOfPreFundedWarrantsShares_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_ExerciseOfPreFundedWarrantsShares_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_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_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_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="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_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss per share of common stock, basic (in dollars 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/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/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/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_WarrantIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Warrant Issuance Costs</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_WarrantIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Warrant Issuance Costs</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_WarrantIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Warrant issuance costs.</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_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_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_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="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="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/terseLabel">Legal settlement</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_AdjustmentsToAdditionalPaidInCapitalWarrantIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of pre-funded warrants, net of issuance cost of $283</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalWarrantIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustments to Additional Paid in Capital, Warrant Issued</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="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="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="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_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_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_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Cash Provided by (Used in) Operating Activities</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="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/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/verboseLabel">Tranche B Term Loan</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SaleOfStockExercisePriceOfWarrantsOrRights_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pre-funded warrant price (in dollars per share)</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SaleOfStockExercisePriceOfWarrantsOrRights_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale Of Stock Exercise Price Of Warrants Or Rights</link:label>
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    <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>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtConversionNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Conversion, Name [Domain]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtConversionNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Conversion, Name [Domain]</link:label>
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    <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 of common stock, diluted (in dollars per share)</link:label>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_StockIssuedDuringPeriodValueWarrantsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period Value Warrants Exercised</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_StockIssuedDuringPeriodValueWarrantsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Stock issued during period value warrants exercised.</link:label>
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    <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_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_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_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_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_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="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_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_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/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_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/terseLabel">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/label">Entity Address, Postal Zip Code</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="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="us-gaap_GranteeStatusDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Grantee Status [Domain]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GranteeStatusDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Grantee Status [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_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_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="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_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_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="dei_EntityIncorporationStateCountryCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Incorporation, State or Country Code</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityIncorporationStateCountryCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Incorporation, State or Country Code</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_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="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_PensionAndOtherPostretirementBenefitsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Retirement Plan</link:label>
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    <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 pre-funded warrants, net of issuance costs</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="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="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="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="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_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="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_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_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_RestrictedCashCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Insurance recovery of legal settlement</link:label>
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    <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_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_NotesPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current loan payable</link:label>
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    <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>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition</link:label>
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    <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>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ConversionOfPreferredStockIntoAShareOfCommonStockMemberMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Conversion Of Preferred Stock Into A Share Of Common Stock</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ConversionOfPreferredStockIntoAShareOfCommonStockMemberMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Conversion Of Preferred Stock Into A Share Of Common Stock Member [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ConversionOfPreferredStockIntoAShareOfCommonStockMemberMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Conversion Of Preferred Stock Into A Share Of Common Stock Member</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ConversionOfPreferredStockIntoAShareOfCommonStockMemberMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Conversion of Preferred Stock into a Share of Common Stock</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_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_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_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_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="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="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_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/documentation">South San Francisco California Member</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="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="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_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Cash Provided by (Used in) Operating Activities [Abstract]</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="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/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/verboseLabel">Thershold index rate</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_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_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 stock</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="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/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/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/2009/role/negatedTerseLabel">Less accumulated depreciation</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/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/totalLabel">General and Administrative Expense, Total</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_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_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_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_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted-average shares of common stock outstanding, basic (in shares)</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 of common stock outstanding, basic (in shares)</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/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="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_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Cash Provided by (Used in) Financing Activities [Abstract]</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="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/documentation">2019 Employee Stock Purchase Plan</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="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/terseLabel">Accrued clinical trial liability</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_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_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_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_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_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="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="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="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="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_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">2025</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_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_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_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="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="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/documentation">Brisbane California.</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_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="tpst_PrivateTempestPreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Private tempest preferred stock.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PrivateTempestPreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Private Tempest Preferred Stock [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PrivateTempestPreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Private Tempest Preferred 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="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_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_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="tpst_StockIssuedDuringPeriodSharesWarrantsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercise of common stock warrants (in shares)</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_StockIssuedDuringPeriodSharesWarrantsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period Shares Warrants Exercised</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_StockIssuedDuringPeriodSharesWarrantsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Stock issued during period shares warrants exercised.</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_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalents, at Carrying Value</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="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="tpst_StockIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">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/documentation">Stock Issuance Costs.</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_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_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_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_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_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/totalLabel">Prepaid Expense, Current, Total</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="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="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_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="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="tpst_PrivateInvestmentInPublicEntityFinancingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">PIPE Financing</link:label>
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    <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="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="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_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, expiration period</link:label>
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    <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="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/documentation">Unaudited Interim Financial Statement, Policy</link:label>
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    <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="tpst_IndividualsWhoWereNotPreviouslyEmployeesOrDirectorsOfCompanyMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Individuals who were not Previously Employees or Directors of Company</link:label>
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    <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>
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    <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/periodStartLabel">Property, Plant and Equipment, Gross, Beginning Balance</link:label>
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    <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>
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    <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_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_WeightedAverageNumberOfSharesOutstandingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Denominator:</link:label>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercise of stock options</link:label>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityEmergingGrowthCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Emerging Growth Company</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityEmergingGrowthCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Emerging Growth Company</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_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="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="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="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Accrued Expenses</link:label>
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    <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>
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    <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>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2023 (excluding six months ended June 30, 2023)</link:label>
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    <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>
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    <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 Equivalents, Restricted Cash, and Restricted Cash Equivalents</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_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="tpst_Ecor1CapitalLlcAndVersantVentureCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">EcoR1 Capital LLC and Versant Venture Capital.</link:label>
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    <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>
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    <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="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Small Business</link:label>
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    <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>
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    <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>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SaleOfStockAmountAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock, Amount Authorized</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SaleOfStockAmountAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Sale of Stock, Amount Authorized</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/label">Supplemental Balance Sheet Disclosures [Text Block]</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>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalLeaseObligationsIncurred_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lease modification</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalLeaseObligationsIncurred_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease Obligation Incurred</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="us-gaap_IncomeStatementLocationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Statement Location [Axis]</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="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/documentation">ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAssumedInReverseRecapitalizationInPeriod</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_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_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_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_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="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/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_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_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_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="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_AdjustmentsToAdditionalPaidInCapitalShareBasedCompensationStockOptionsRequisiteServicePeriodRecognition_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation</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="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="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="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_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_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_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="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/label">Two Thousand Twenty Three Inducement Plan [Member]</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="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_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Cash Provided by (Used in) Investing Activities [Abstract]</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="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/terseLabel">Amended and Restated 2019 Equity Incentive Plan</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="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_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_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/terseLabel">Net of discount and issuance costs, Current</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="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/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/verboseLabel">Term Loan</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_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_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_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/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/verboseLabel">Interest expense</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_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_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_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/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/periodEndLabel">Common Stock, Shares, Outstanding, Ending Balance</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_DebtConversionByUniqueDescriptionAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Conversion Description [Axis]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtConversionByUniqueDescriptionAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Conversion Description [Axis]</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_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_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_IncomeStatementLocationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Statement Location [Domain]</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_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="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="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="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_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Cash Provided by (Used in) Investing Activities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentQuarterlyReport_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Quarterly Report</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>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_LesseeOperatingLeaseLiabilityToBePaidDueAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2026 and beyond</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_LesseeOperatingLeaseLiabilityToBePaidDueAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Due After Year Four</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_LesseeOperatingLeaseLiabilityToBePaidDueAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lessee, Operating Lease, Liability, to be Paid, Due After Year Four</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="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="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_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/verboseLabel">Annual floating interest rate</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lessee operating lease liability payments due after year four.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee Operating Lease Liability Payments Due After Year Four</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2028 and beyond</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_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/documentation">NumberOfNonCancelableOperatingLeaseAgreements</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 financing activities</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">Net Cash Provided by (Used in) Financing Activities</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_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="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="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="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_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/totalLabel">Total other income (expense), net</link:label>
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    <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>
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