Due to superior material properties of SiC for high-voltage devices, SiC Schottky diodes are used in energy-conversion systems such as solar-cell inverters, battery chargers, and power modules for electric cars and unmanned aerial vehicles. The reliable operation of these systems requires the chip temperature of SiC Schottky diodes to be maintained within the limit set by the device package. This is especially crucial during surge-current events that dissipate heat within the device. As a thermal-management method, manufactures of commercial SiC Schottky diodes have introduced wafer thinning practices to reduce the thickness of the SiC chip and, consequently, to reduce its thermal resistance. However, this also leads to a reduction in the thermal capacitance. In this paper, we present experimental data and theoretical analysis to demonstrate that the reduced thermal capacitance has a much larger adverse effect in comparison to the beneficial reduction of the thermal resistance. An implication of the presented results is that, contrary to the adopted wafer thinning practices, SiC Schottky diodes fabricated without wafer thinning have superior surge-current capability.