We performed molecular dynamics simulations of the vaporization phenomenon of an ultra-thin layer (2 nm) of liquid argon on a platinum surface. The simulation started from a molecular system of three phases (liquid argon, solid platinum and argon vapor) in equilibrium at 110 K. The platinum wall was then suddenly heated to a higher temperature (a moderately higher temperature of 150 K and a much higher temperature of 300 K were investigated). Features of our simulation model include a fast algorithm based on a tree data structure and a constant temperature solid wall model based on a 3-D Langevin equation. The entire vaporization process was successfully simulated. The results reveal trends that agree with our knowledge of vaporization of a similar macroscopic system. For example, for the high surface temperature the vaporization process is reminiscent of the Leidenfrost phenomenon and after the formation of a vapor region between the surface and the liquid mass, the latter deforms and tends to approximately acquire a spherical "droplet" shape, as one would have expected from macroscopic considerations. Contrary to this, a gradual evaporation process occurs at moderate wall temperatures. After complete evaporation and upon reduction of the wall temperature, condensation takes place leading to reconstruction of the initial liquid layer.