This study addresses the thermal hazards that arise during the initial engagement stage of wet clutches, where rapid heat generation within the transient lubricating film may cause premature film rupture, torque instability, and accelerated wear. To overcome these challenges, a coupled thermo–fluid model was developed to capture oil film flow, heat transfer, and viscous torque behavior under varying groove structures. A novelty of this work is the first integration of computational fluid dynamics (CFD) with response surface methodology (RSM) to systematically reveal how groove geometry—cross-sectional shape, number, and inclination angle—collectively influences peak temperature and viscous torque during the lubricating film stage. Simulation results show that spiral semi-circular grooves provide superior thermal management, reducing the peak friction plate temperature to 75.5 °C, while the optimized design obtained via RSM (groove depth of 0.89 mm, 19 grooves, and a 5.28° inclination angle) further lowers the maximum temperature to 68.2 °C and sustains torque transmission above 18.5 N·m. These findings demonstrate that rational groove design, guided by multi-objective optimization, can mitigate thermal risks while maintaining torque stability, offering new insights for the high-performance design of wet clutches.