We present results of an ab initio study of the structural and thermoelastic properties of orthorhombic (Pbnm) MgSiO₃ perovskite as a function of temperature and pressure. Self‐consistent free energies are computed using quasiharmonic lattice dynamics with interatomic potentials derived from an electron‐gas formulation. At high temperatures the orthorhombic phase undergoes successive second‐order transitions to tetragonal and cubic phases. The transition temperatures increase with pressure such that the orthorhombic phase is stable throughout most of the lower mantle although the higher symmetry phases could occur near the top of the lower mantle. At zero pressure the calculated bulk modulus and thermal expansion are in excellent agreement with the available data. We find that for high‐temperature isotherms, a finite‐strain decompression of the high‐pressure equation of state of perovskite substantially overestimates its zero‐pressure density and bulk modulus; hence, constraints on the chemical composition of the lower mantle, based on a comparison of the decompressed seismological properties with zero‐pressure laboratory data may significantly overestimate the proportion of perovskite in the lower mantle.