The dynamics of the intermolecular short hydrogen bond in the molecular complex of urea and phosphoric acid are investigated using plane-wave density functional theory. Results indicate migration of the proton toward the center of the hydrogen bond as temperature is increased, in line with recent experimental measurements. Computed vibrational frequencies show favorable agreement with experimental measurement. An analysis of existing neutron diffraction data leads us to conclude that the effective potential well experienced by the proton is temperature-dependent. Inspired by our computations and theoretical analysis, we offer a possible explanation for the proton migration phenomenon.