  The accuracy of a model to describe the horizontal dynamics of a confined
quasi-two-dimensional system of inelastic hard spheres is discussed by
comparing its predictions for the relaxation of the temperature in an
homogenous system with molecular dynamics simulation results for the original
system. A reasonably good agreement is found. Next, the model is used to
investigate the peculiarities of the nonlinear evolution of the temperature
when the parameter controlling the energy injection is instantaneously changed
while the system was relaxing. This can be considered as a non-equilibrium
generalization of the Kovacs effect. It is shown that, in the low density
limit, the effect can be accurately described by using a simple kinetic theory
based on the first Sonine approximation for the one-particle distribution
function. Some possible experimental implications are indicated.
