A novel thermal management approach is explored, which uses supercritical carbon dioxide (sCO2) as a working fluid to manage extreme heat fluxes in electronics cooling applications. In the pseudocritical region, sCO2 has extremely high volumetric thermal capacity, which can enable operation with low pumping requirements, and without the potential for two-phase critical heat flux (CHF) and flow instabilities. A model of a representative microchannel heat sink is evaluated with single-phase liquid water and FC-72, two-phase boiling R-134a, and sCO2. For a fixed pumping power, sCO2 is found to yield lower heat-sink wall temperatures than liquid coolants. Practical engineering challenges for supercritical thermal management systems are discussed, including the limits of predictive heat transfer models, narrow operating temperature ranges, high working pressures, and pump design criteria. Based on these findings, sCO2 is a promising candidate working fluid for cooling high heat flux electronics, but additional thermal transport research and engineering are needed before practical systems can be realized.