We examine various formulations for the numerical resolution of interface problems with compressible fluids. The difficulty with this type of problem resides in the computation of the thermodynamic variables inside the numerical diffusion zone at the interfaces. Indeed, any Eulerian numerical scheme produces artificial diffusion zones at the interfaces and produces consequently an artificial mixture for which the determination of thermodynamic variables is difficult. All inaccuracy in their determination induces failure of the computation (negative pressure or negative argument in the sound speed computation). Moreover, these models and methods have never been examined for the temperature computation. The examination of their drawbacks results in the rejection of some of them and to the proposition of a very efficient new model. This model is presented with its own numerical method. We then explain the way to solve for heat diffusion at the interface and give a computational example in two dimensions, The evaluation of these models is achieved over a series of problems with exact solutions.