In-situ neutron and X-ray diffraction experiments were used to determine the crystal structure of Ba2In2O5 as related to temperature. Ba2In2O5 has a Brownmillerite-type crystal structure from room temperature to 900 degreesC, consisting of an orthorhombic unit cell with lattice parameters 6.0864(3) X 16.7903(7) X 5.9697(3) Angstrom and 1cmm (74) space group symmetry. At 900 degreesC, oxygen vacancies begin to disorder. By 925 degreesC, barium indate crystallizes in a tetragonal, 6.0348(4) X 17.0688(22) Angstrom, unit cell with 14cm (108) space group symmetry. This oxygen vacancy order-disorder transition is associated with an evolution to fast oxide-ion conduction. At 1040 degreesC, Ba2In2O5 becomes a cubic oxygen-deficient perovskite, 4.2743(1) Angstrom, in the Pm3m space group. At 1080 degreesC, Ba2In2O5 begins to decompose.