An ITC (independently tunable cells) thermionic RF gun has been developed as the electron source for coherent terahertz radiations at Tohoku University. Both experiments and simulations have shown that the back-bombardment (B.B.) effect on the LaB6 cathode is a serious issue for stable operation. A numerical model has been developed to evaluate the increase of the cathode temperature due to B.B. in which the 2D equation for heat conduction is solved by taking the back-streaming electrons into account. Using this model we have studied the possibility of suppressing the B.B. by imposing external dipole field and by optimization of the cathode size, compared with experimental data. The results will be reported here.