Demanding accuracy and reliability of thermal design for high efficiency and high-power density inverter devices. Integrating heat conduction, convection heat transfer and fluid dynamics theories, a synthetical thermal model based on the characteristic length as the square root of the cross-sectional area and a multi-objective optimization method based on entropy yield minimization theory and electrothermal coupling are proposed for a typical forced air-cooling heatsink system to improve the efficiency of design optimizations in the structure and cost. The fin thickness, fin length, number of fins, and air velocity of the heatsink are used as design variables, and the NSGA-III algorithm applying a prophet population is used to obtain the pareto fronts with minimum thermal resistance, cost and pressure loss as optimization objectives. Enhanced airflow through the heatsink by arranging the columns in a phyllotactic pattern. A temperature rise test by a 100 V/10 kW prototype was designed to prove the accuracy of the model proposed and heatsink optimized. At rated power, the surface temperature of power devices and heatsink has 10 °C reduction.