In recent studies, it was reported that there existed the temperature discontinuity at a liquid-vapor interface in an equilibrium state. However, from the viewpoint of the classical thermodynamics, it is highly questionable result although considering that the experiments related with a boundary layer is very difficult due to the extremely thin thickness of it. To clarify whether the temperature discontinuity over a liquid-vapor interface really exists, the computer simulations were performed. From the simulation results, it could be concluded that the misconception in a temperature calculation might result in non-uniform temperature distributions over an interface under an equilibrium state