To study the crystallography of Earth’s lower mantle, techniques for measuring synchrotron x-ray diffraction from a laser-heated diamond anvil cell have been developed. Experiments on samples of (Mg,Fe)SiO3 show that silicate perovskite maintains its orthorhombic symmetry at 38 gigapascals and 1850 kelvin. Measurements at 65 and 70 gigapascals provide evidence for a temperature-induced orthorhombic-to-cubic phase transition and dissociation to an assemblage of perovskite and mixed oxides. If these phase transitions occur in Earth, they will require a significant change in mineralogical models of the lower mantle.