We present a model study of the vibrational excitation of NO molecules scattering from a Ag(111) surface using time-dependent wave packet methods. The molecule-surface interaction is described by a two-dimensional potential energy surface in the vibrational and center-of-mass coordinates. Surface motion is modeled by a single atomic oscillator This model reproduces the experimentally observed increase in the vibrational excitation as a function of both increasing initial translational energy of the molecule and surface temperature. The surface temperature only enters via the Boltzmann weighting of initial surface vibrational states. We simplify the simulation to a two-dimensional surface-mass model, where the gas-surface interaction is analogous to a classical "cube" model. It is shown that the relative velocity of the incoming molecule, with respect to the surface, causes the observed dependence of the vibrational excitation on surface temperature. The savings in computational time achieved with this model allows a study of the effect of the potential topology and surface mass on the temperature dependence of the vibrational excitation.