Materials showing negative thermal expansion (NTE) coefficient over large temperature ranges are nowadays of great interest for their possible applications. Small nanoparticles show changes in their properties with respect to the corresponding bulk, mainly due to the high surface to volume ratio and to the confinement of electrons in a small volume. In the present paper we report a x-ray absorption fine structure (XAFS) study on the thermal expansion coefficient of an Au foil and of Au nanoparticles of very small dimensions ranging from 2.4 nm and 5.0 nm. Their L₃ edge has been investigated in the temperature range 20K – 300K and a very accurate data analysis has been performed taking into account the presence of asymmetry effects. All clusters showed a thermal trend of the first shell distance significantly different from that of the bulk. The larger clusters were characterized by a reduction of the thermal expansion coefficient with respect to bulk; in the smallest samples the crossover from a thermal expansion to a NTE effect was observed. A simple model, based on the contribution of localized states induced by the finite size of the clusters, qualitatively accounts for the observed behaviour.