The increasing need for higher power density and closer integration of power subsystems consisting of superconducting motors/generators, degaussing coils, energy storage modules, and cables leads one to consider the merits of refrigerating the associated power electronics down to cryogenic temperatures. High temperature superconducting (HTS) components combined with cryogenic power converters resulting in high power density power conversion systems will have a significant effect on several industrial, commercial, transportation, and renewable energy applications. Cryogenic power converters provide promising benefits over their room temperature counterparts in terms of reduced size and weight due to increased power density, improved efficiency, switching speed, and reliability. Integration could result in significant weight and space savings for the overall system. In this paper, a conceptual design study on the wide-bandgap-based (especially SiC and GaN) MW-class power inverter/converter is reported. Based on the total power loss of the designed converter, different cryogenic cooling strategies are proposed. The cooling power requirements, cooler mass, the cooler cost is evaluated based on the operating temperature of MW-class power converter. Finally, a power density comparison for different types of conventional power applications and HTS applications together with MW-class power converters is presented. The future of the cryogenically cooled power electronics system together with superconducting power devices is described for large-scale applications such as for future electric aircraft.