Thermal management of Li-ion batteries is important because of the high energy content and the risk of rapid temperature development in the high current range. Reliable and safe operation of these batteries is seriously endangered by high temperatures. It is important to have a simple but accurate model to evaluate the thermal behavior of batteries under a variety of operating conditions and be able to predict the internal temperature as well. To achieve this goal, a radial-axial model is developed to investigate the evolution of the temperature distribution in cylindrical Li-ion cells. Experimental data on LiFePO4 cylindrical Li-ion batteries are used to determine the overpotentials and to estimate the State-of-Charge-dependent entropies from the previously developed adaptive thermal model . The heat evolution is assumed to be uniform inside the battery. Heat exchange from the battery surfaces with the ambient is non-uniform, i.e. depends on the temperature of a particular point at the surface of the cell. Furthermore, the model was adapted for implementation in battery management systems. It is shown that the model can accurately predict the temperature distribution inside the cell in a wide range of operating conditions. Good agreement with the measured temperature development has been achieved. Decreasing the heat conductivity coefficient during cell manufacturing and increasing the heat transfer coefficient during battery operation suppresses the temperature evolution. This modified model can be used for the scale-up of large size batteries and battery packs.