A new approach for measuring the thermal resistance of power field-effect transistors (FETs) with extremely high spatial resolution below 40 nm has been demonstrated using cathodoluminescence generated by a low-energy electron beam. The energy shift of the fundamental bandgap caused by the current heating in the channel region is spatially probed, and is converted to the channel temperature using the temperature dependence of the material bandgap. The obtained thermal resistances of the GaAs metal semiconductor field effect transistor (MESFET) and the GaN MESFET are compared with those measured by the conventional electrical technique.