The crystal structure of the technologically relevant, high-temperature proton conductor BaZr_0.7Ce_0.2Y_0.1O_3-δ (BZCY72) has been studied by high-resolution neutron powder diffraction performed on a deuterated sample in the temperature range 10.1173 K, complemented with synchrotron X-ray diffraction in the range RT-1173 K. A volume discontinuity on heating indicates a first-order phase transition from orthorhombic (space group Imma) to rhombohedral symmetry (R3c) between 85 and 150 K. A further transition to cubic symmetry (Pm3m) takes place at ∼570 K, indicated to be second order from the temperature dependence of the octahedral tilt angle. The stability field of the cubic phase was extended on cooling in the dehydrated state to 85 K. Expansion/contraction of the unit-cell volume on heating in low vacuum and air, respectively observed by neutron diffraction and synchrotron X-ray diffraction, was described with a point-defect model involving the temperature dependence of the water content and thermal expansion. Isotropic strain in the hydrated state is apparent on analysis of the broadening of the neutron-diffraction reflections during heating and cooling cycles. Rietveld refinement of the low-temperature neutron data and Fourier nuclear-density maps were employed to locate the deuterium position at a distance of ∼0.90 Å from the bonding oxygen at 10 K.