Non-equilibrium molecular dynamics (NEMD) simulations have been carried out to obtain new evidence for the inverted temperature profile. We find that the inverted temperature profile occurs due to the excess energy transported by the reflecting molecules. A new definition of the accommodation coefficient for the reflecting molecule is proposed based on the comparison of the energy transferred by the reflecting molecule between the equilibrium and non-equilibrium conditions. The accommodation coefficient decreases with increasing the mass flux in the vicinity of the liquid surface and this is the reason for the inverted temperature profile. Also, a direct simulation of Monte Carlo (DSMC) method has been performed by applying the molecular boundary condition developed in the non-equilibrium molecular dynamics simulation. An inverted temperature profile is obtained without any contradiction to the second law because the reflecting molecules cannot accommodate to the equilibrium state.