In this study, the thermal and hydraulic performance of a lithium-ion battery thermal management system incorporating a microchannel heat sink with a water–Al₂O₃ nanofluid (2% volume fraction) and metal foam was numerically investigated at discharge rates of 3C–5C. The battery system consists of four series-connected cells, each with a capacity of 14.6 Ah and dimensions of 145×192×4.5 mm. The cooling system comprises seven horizontally arranged microchannels with a 2×2 mm cross-section, uniformly spaced across the heat sink surface. The battery was modeled using the MSMD approach coupled with the NTGK electrochemical submodel, while the metal foam was modeled based on the Darcy–Brinkman–Forchheimer equations. The effects length and location of metal foam on the BTMS performance were investigated. The results showed that placing the metal foam toward the downstream end of the microchannels reduced the maximum battery temperature and temperature difference by up to 9% and 48%, respectively, relative to its placement near the inlet, while maintaining a nearly unchanged pressure drop. Subsequently, the metal foam length in each microchannel was independently optimized using a multi-objective approach, and the optimal design was selected using TOPSIS with entropy weighting. The optimized configuration reduced the maximum temperature and temperature difference by approximately 70% and 80%, respectively, compared with the no cooling case, and significantly improved performance over the uniform foam-length configuration.