Metal–oxide–semiconductor field-effect transistors (MOSFETs) are critical in power electronic modules due to their high-power density and rapid switching capabilities. Therefore, effective thermal management is crucial for ensuring reliability and superior performance. This study used finite element analysis (FEA) to evaluate the electro-thermal behavior of MOSFETs with copper clip bonding, showing a significant improvement over aluminum wire bonding. The aluminum wire model reached a maximum temperature of 102.8 °C, while the copper clip reduced this to 74.6 °C. To further optimize the thermal performance, Latin Hypercube Sampling (LHS) generated diverse design points. The FEA results were used to select the Kriging regression model, chosen for its superior accuracy (MSE = 0.036, R2 = 0.997, adjusted R2 = 0.997). The Kriging model was integrated with a Genetic Algorithm (GA), further reducing the maximum temperature to 71.5 °C, a 4.20% improvement over the original copper clip design and a 43.8% reduction compared to aluminum wire bonding. This integration of Kriging and the GA to the MOSFET copper clip package led to a significant improvement in the heat dissipation and overall thermal performance of the MOSFET package, while also reducing the computational power requirements, providing a reliable and efficient solution for the optimization of MOSFET copper clip packages.