The thermal performance of a lithium-ion battery module comprising three cells contained within a casing was investigated at discharge rates of 3C and 5C with three different cooling strategies: forced air, phase-change material (PCM), and a hybrid system using a combination of forced air and the PCM. Three levels of fan speed (5000 rpm; 7000 rpm; and 9000 rpm) for cooling air flow were considered. A numerical simulation of heat transfer was performed using the ANSYS Fluent software. The electrochemical modelling of a battery was developed based on the NTGK approach, and the phase-change phenomenon was treated as an enthesis–porosity problem. The composite PCM, aluminum metal foam embedded in n-octadecane, had better heat dissipation performance than forced air convection. The PCM is significantly more effective at heat dissipation than forced air. Interestingly, when using a hybrid cooling system that combines forced air and a PCM, although it meets the operational requirements for Li-ion batteries in regard to maximum temperature and temperature uniformity at a 3C discharge rate, the airflow appears to have a negligible effect on thermal management and yields an indiscernible change in temperature. This can be attributed to a complex flow pattern that developed in a casing as a result of the suboptimal design of the inlet and outlet. Further studies will be required for the optimal positioning of the inlet and outlet, as well as the effectiveness of combining liquid cooling methods.