Two models are presented to predict the thermal behavior of the lithium/polymer battery. Part I presents the one-cell model, a one-dimensional model for predicting the thermal behavior of the lithium negative electrode/solid polymer separator/insertion positive electrode cell. Part II presents the cell-stack model, a one-dimensional model that uses variable heat-generation rates calculated by the one-cell model to predict temperature profiles in cell stacks. The one-cell model, presented in Part I, is based on the model of Doyle et al.(1) with the addition of an energy balance in the form given by Bernardi et al.(2) Physical properties are allowed to vary with temperature. The model is general and can be used to simulate a wide range of polymeric separator materials, lithium salts, and composite insertion electrodes. Simulation results for the LiPEO(15)-LiCF3SO3TiS2 system are presented for isothermal operation at several temperatures and adiabatic operation at several discharge rates. Heat transfer to the surroundings is considered by defining a position-dependent heat-transfer coefficient for various cells in a cell stack.