This paper proposes a rapid tritium accounting method that will enhance the tritium accountability of a tritium storage and delivery system (SDS) with in-bed calorimetry. We derive an accounting model with validation of assumptions based on the law of Newton's cooling. The characteristics of the accounting model enable rapid accounting by instantly measuring the temperature gradient of a tritium storage bed in natural cooling. We validate the accounting method with experiments that demonstrate a good trackability for tritium inventory in the storage bed. Further research with a dedicated design for the proposed method is necessary to improve the rapidity and accuracy of the SDS.