Deuterated 3,5-pyridinedicarboxylic acid exhibits reversible temperature-induced deuteron migration of a magnitude unprecedented in this class of compounds. We used a combination of variable-temperature powder and single-crystal neutron diffraction and density functional theory (DFT)-based computational methods to elucidate the origin of this remarkable behaviour. Single-crystal neutron diffraction shows that between 15 and 300 K, the deuteron moves by 0.32(1) Å and the structure changes from a low-temperature ND⋅⋅⋅O form to a high-temperature N⋅⋅⋅DO form. Variable-temperature powder neutron-diffraction data, which was fitted by using parametric Rietveld refinement, show that this deuteron migration is due to an isosymmetric, first-order phase transition that occurs by growth of the daughter phase in the parent-phase matrix. Similar phase transitions are observed in two selectively deuterated forms of the material. DFT calculations demonstrate the role of phonons and show that vibrational free-energy stabilisation, which plays a key role in the observed structural phase transitions, is more pronounced in the fully deuterated material and proportional to the mass of the molecule, that is, the level of deuteration. This is consistent with our experimental work, for which distinct crystallographic phase transitions were clearly observed for the three deuterated systems, but not for the fully protonated material.