Information on protein internal motions is usually obtained through the analysis of atomic mean-square displacements, which are a measure of variability of the atomic positions distribution functions. We report a statistical approach to analyze molecular dynamics data on these displacements that is based on probability distribution functions. Using a technique inspired by the analysis of variance, we compute unbiased, reliable mean-square displacements of the atoms and analyze them statistically. We applied this procedure to characterize protein thermostability by comparing the results for a thermophilic enzyme and a mesophilic homolog. In agreement with previous experimental observations, our analysis suggests that the proteins surface regions can play a role in the different thermal behavior.