A rigorous three-dimensional analytical model is proposed to investigate thermal response of batteries to transient heat generation during their operation. The modeling is based on integral-transform technique that gives a closed-form solution for the fundamental problem of heat conduction in battery cores with orthotropic thermal conductivities. The method is examined to describe spatial and temporal temperature evolution in a sample prismatic lithium-ion battery (EiG ePLB C020), subjected to transient heat generation in its bulk, and various convective cooling boundary conditions at its surfaces (the most practical case is considered, when surrounding medium is at a constant ambient temperature). The full-field solutions take the form of a rapidly converging triple infinite sum whose leading terms provide a very simple and accurate approximation of the battery thermal behavior. A surface-averaged Biot number has been proposed that can simplify the thermal solutions under certain conditions. The presented analytical model provides a fast yet accurate tool for battery thermal management system designs.