Abstract The aim of this work is to realize a new numerical program based on the development of a mathematical model allowing determining the parameters of the supersonic flow through a conical shock under hypothesis at high temperature, in the context of correcting the perfect gas model. In this case, the specific heat at constant pressure does not remain constant and varies with the increase of temperature. The stagnation temperature becomes an important parameter in the calculation. The mathematical model is presented by the numerical resolution of a system of first-order nonlinear differential equations with three coupled unknowns for initial conditions. The numerical resolution is made by adapting the higher order Runge Kutta method. The parameters through the conical shock can be determined by considering a new model of an oblique shock at high temperature. All isentropic parameters of after the shock flow depend on the deviation of the flow from the transverse direction. The comparison of the results is done with the perfect gas model for low stagnation temperatures, upstream Mach number and cone deviation angle. A calculation of the error is made between our high temperature model and the perfect gas model. The application is made for air.