We present local density approximation augmented by the Hubbard-type correction calculations of high-temperature elastic properties of bridgmanite with composition (Mg(1-x)Fex2+)SiO3 for 0 <= x <= 0.125. Results of elastic moduli and acoustic velocities for the Mg end-member (x=0) agree very well with the latest high-pressure and high-temperature experimental measurements. In the iron-bearing system, we focus particularly on the change in thermoelastic parameters across the state change that occurs in ferrous iron above similar to 30GPa, often attributed to a high-spin (HS) to intermediate-spin (IS) crossover but explained by first-principles calculations as a lateral displacement of substitutional iron in the perovskite cage. We show that the measured effect of this change on the equation of state of this system can be explained by the lateral displacement of substitutional iron and not by the HS to IS crossover. The calculated elastic properties of (Mg0.875Fe0.1252+)SiO3 along an adiabatic mantle geotherm somewhat overestimate longitudinal velocities but produce densities and shear velocities quite consistent with the Preliminary Reference Earth Model data throughout most of the lower mantle.