We present a complete and detailed thermal simulator designed for the computational analysis of thermal batteries from the level of a single cell up to that of the entire system. Our simulator is based on a comprehensive transient and two-dimensional (axisymmetric) mathematical heat-transfer model, with significant flexibility in the geometrical modeling and the materials used. The model accounts for different aspects of heat transfer, including conduction, joule heating, heat of reactions, and latent heat of fusion associated with electrolyte phase change (salt solidification). It is supported by a simplified mass balance involving the current drawn from the battery and accounting for the mass-transfer resistance of each of the cell's components. Results presented include model verification-and-validation calculations as well as single-cell thermal battery simulations performed under realistic operating conditions. The latter reveal the significance of the phase-change process to heat transfer and thus to the prediction of its operation time. Solidification dynamics are found to be different in each of the cell's components, emphasizing the necessity of accounting for details at the subcell level. Additional results uncover the effect of heat of reactions as well as joule heating on single-cell battery thermal behavior.