Measurements of the intrinsic emittance and transverse momentum distributions obtained from a metal (antimony thin film) photocathode near and below the photoemission threshold are presented. Measurements show that the intrinsic emittance is limited by the lattice temperature of the cathode as the incident photon energy approaches the photoemission threshold. A theoretical model to calculate the transverse momentum distributions near this photoemission threshold is presented. An excellent match between the experimental measurements and the theoretical calculations is demonstrated. These measurements are relevant to low emittance electron sources for Free Electron Lasers and Ultrafast Electron Diffraction experiments.