Increasingly, military and civilian applications of electronics require extremely high-heat fluxes on the order of . Thermal management solutions for these severe operating conditions are subject to a number of constraints, including energy consumption, controllability, and the volume or size of the package. Calculations indicate that the only possible approach to meeting this heat flux condition, while maintaining the chip temperature below , is to utilize refrigeration. Here, we report an initial thermodynamic optimization of the refrigeration system design. In order to hold the outlet quality of the fluid leaving the evaporator to less than approximately 20%, in order to avoid reaching critical heat flux, the refrigeration system design is dramatically different from typical configurations for household applications. In short, a simple vapor-compression cycle will require excessive energy consumption, largely because of the additional heat required to return the refrigerant to its vapor state before the compressor inlet. A better design is determined to be a “two-loop” cycle, in which the vapor-compression loop is coupled thermally to a pumped loop that directly cools the high-heat-flux chip.