Recent neutron diffraction data have shown that the hydrogen atom involved in the short, strong hydrogen bond in urea-phosphoric acid migrates toward the midpoint of the hydrogen bond as the temperature increases. With the help of solid state all initio, calculations and inelastic neutron scattering, we have investigated the temperature dependence of the structural and vibrational properties of the system. The potential energy surface of the proton in the short, strong hydrogen bond and the thermal population of the energy levels therein cannot account for the observed proton migration. Ab initio molecular dynamics simulations clearly reveal the migration of the proton. This molecular dynamics result was reported recently by other authors, but they only offered a tentative explanation in terms of a resonance between high-frequency vibrations, which is not supported by the calculations presented here. We explain the proton migration in terms of phonon-driven structural fluctuations and their impact on the temperature-dependent evolution of the potential energy surface of the short hydrogen-bond proton.