The complex electron-phonon interaction occurring in bulk lead halide perovskites gives rise to anomalous temperature dependences, like the widening of the electronic band gap as temperature increases. However, possible confinement effects on the electron-phonon coupling in the nanocrystalline version of these materials remain unexplored. Herein, we study the temperature (ranging from 80 K to ambient) and hydrostatic pressure (from atmospheric to 0.6 GPa) dependence of the photoluminescence of ligand-free methylammonium lead triiodide nanocrystals with controlled sizes embedded in a porous silica matrix. This analysis allowed us to disentangle the effects of thermal expansion and electron-phonon interaction. As the crystallite size decreases, the electron-phonon contribution to the gap renormalization gains in importance. We provide a plausible explanation for this observation in terms of quantum confinement effects, showing that neither thermal expansion nor electron-phonon coupling effects may be disregarded when analyzing the temperature dependence of the optoelectronic properties of perovskite lead halide nanocrystals.