We investigate the kinetics of enthalpy recovery in stacked glassy polystyrene (PS) films with thickness from 30 to 95 nm over a wide temperature range below the glass transition temperature (Tg). We show that the time evolution toward equilibrium exhibits two mechanisms of recovery, in ways analogous to bulk PS. The fast mechanism, allowing partial enthalpy recovery toward equilibrium, displays Arrhenius temperature dependence with low activation energy, whereas the slow mechanism follows pronounced super-Arrhenius temperature dependence. In comparison to bulk PS, the time scales of the two mechanisms of recovery are considerably shorter and decreasing with the film thickness. Scaling of the equilibration times at various thicknesses indicates that the fast mechanism of recovery is compatible with the free volume holes diffusion model. Conversely, the slow mechanism of recovery appears to be accelerated with decreasing thickness more than predicted by the model and, therefore, its description requires additional ingredients. The implications, from both a fundamental and technological viewpoint, of the ability of thin polymer films to densify in relatively short time scales are discussed.