The thermodynamic properties of the small-polaron model are studied by means of a discrete version of the Feynman path-integral representation of the partition function. This lattice model describes a fermion interacting with a boson field. The bosons are treated analytically, the fermion contribution is calculated using a Monte Carlo method. We analyze the thermodynamic functions for the case of one-, two-, and three-dimensional polaron motion. We present strong evidence that the polaron becomes superlocalized if the interaction strength is greater than a critical value.