We used molecular dynamics simulations of a typical monomeric protein, SNase, in combination with Voronoi-Delaunay tessellation to study and analyze the temperature dependence of the apparent volume, Vapp, of the solute. We show that the void volume, VB, created in the boundary region between solute and solvent, determines the temperature dependence of Vapp to a major extent. The less pronounced but still significant temperature dependence of the molecular volume of the solute, VM, is essentially the result of the expansivity of its internal voids, as the van der Waals contribution to VM is practically independent of temperature. Results for polypeptides of different chemical nature feature a similar temperature behavior, suggesting that the boundary/hydration contribution seems to be a universal part of the temperature dependence of Vapp. The results presented here shine new light on the discussion surrounding the physical basis for understanding and decomposing the volumetric properties of proteins and biomolecules in general.