When the stagnation temperature increases, the specific heat does not remain constant and start to vary with this temperature. The gas is perfect; its state equation remains always valid, except, it was called by calorically imperfect gas or gas at high temperature. The purpose of this work is to develop a mathematical model for a normal shock wave at high temperature when the stagnation temperature is taken into account, less than the dissociation of the molecules. A generalisation model for a perfect gas for constant heat specific is obtained. A study on the error given by the perfect gas model compared to our model is presented in order to find a limit of application of the perfect gas model. The application is for air.