With the development of energy storage converters to large capacity and modularity, silicon carbide (SiC) devices have gradually become a research hotspot due to their low loss and high temperature resistance characteristics. However, the high switching speed of SiC devices makes them more sensitive to stray inductance in the circuit, and the high-temperature operating environment also has an impact on the long-term safe and reliable operation of the devices. Therefore, this paper focuses on the low-inductance design and heat dissipation design methods for SiC MOSFET-based energy storage converter power unit, and proposes an overall design scheme for the power unit. By optimizing the structure of the laminated busbar, the stray inductance of the high-voltage AC module and low-voltage DC module is reduced to 794 μH and 235 μH, respectively, which effectively reduces the turn-off overvoltage of the power unit. Through thermal simulation studies, a heat dissipation scheme is established so that the maximum temperature of the device does not exceed 50 °C during operation. Finally, a power unit prototype is built and dragged for experiments to verify the effectiveness of the optimized design of the laminated busbar structure and the power unit thermal design scheme.