Abstract: The flow control mechanism of discharge plasma is divided into two categories, namely, thermal effect and non-thermal effect, and the thermal effect of the discharge plasma has obvious control effect on the shock wave structure of the flow field. In the numerical simulation of the shock wave control using discharge plasma, the local temperature of the surface discharge region can reach above ten thousand degree centigrade or kelvin degree. If not considering the nonlinear change of the specific heat at constant pressure(C_p) with gas temperature in the process of numerical simulation, the result is lack of authenticity. In this article, a Mach 5 supersonic inlet is considered, and the process of shock wave control using surface discharge is numerically simulated. Both constant C_p and varied C_p are considered. Results show that: 1) for both cases, the electric excitation has a significant effect on shock wave control; 2) the temperature associated parameters (temperature, Mach number, total pressure recovery coefficient) are effected to great extent. Therefore, in order to obtain more realistic calculation results of surface plasma for shock wave control, the effect of variation of C_p with temperature should be considered.