Thermionic RF guns are used as highly brilliant electron source for linac-driven FEL (free electron laser). They can potentially produce an electron beam with high energy, small emittance, short pulse duration, inexpensive and compact configuration in comparison with other high brightness electron sources, e.g., DC guns and photocathode RF guns. The most critical issue of the thermionic RF gun is the transient cathode heating problem due to the electron back-bombardment when the gun is used for an FEL driver. The heating property of cathode strongly depends on the physical properties of the cathode material such as electron stopping power and range. We investigated the heating property of six hexaboride materials against the back-bombarding electrons by numerical calculation of the stopping power and range. In this investigation, the emission property of the cathode was also taken into account, since high electron emission is required for generation of high brightness electron beam. As a result, calcium hexaboride material has best properties for thermionic RF gun cathode material in the backbombardment effect point of view.