An ITC (independently tunable cells) RF gun is currently used to produce sub-picosecond electron pulses as part of the injector for coherent terahertz radiation at Tohoku University. Both experiments and simulations of particle tracing by GPT have shown that the back-bombardment(B.B.) effect on the LaB6 cathode's surface is serious and should be controlled carefully. To evaluate the temperature increase due to B.B. a 2D model is created for heat transfer inside the cathode. In the 2D model, the back-streaming electrons are treated as external heat source as well as the cathode heater that heats the cathode from its side along with thermal radiation from its surface. The energy deposit of B.B. inside the cathode is calculated by EGS5 or Geant4 by use of the information of back-streaming electrons derived from GPT simulation. The results of simulation on time dependent evolutions of temperature and emission current density of the cathode caused by B.B. were compared with experimental data.