In ultrathin polymer films, the coupling between the segmental mobility, precursor of the molecular diffusion, and the crystallization rate is broken down because of interfacial interactions. In particular, in the presence of a reduced mobility layer at the interface with the substrate, the crystallization kinetics slow down at a length scale bigger than the one connected with the deviation from bulk behavior of the structural relaxation. By modeling the influence of the substrate interactions on the parameters governing the temperature evolution of the main relaxation time, it was possible to reproduce the effect of geometrical confinement on the quantities connected to the diffusion-limited crystallization rate. Upon reduction of the thickness or increasing of the substrate interaction, the films show an apparent higher glass stability in terms of an increase of the cold crystallization temperature and of the crystallization time. The deviations from bulk behavior were found to vanish above a crossover temperature as already observed for the phenomena connected to the glass transition.