The melting temperature of (Mg,Fe)SiO₃ perovskite, the dominant mineral phase of the Earth's lower mantle, has been measured to a pressure of 96 (±10) GPa. Below 60 GPa we find good agreement with the previous measurement of Heinz and Jeanloz [1987a], and above 60 GPa the melting curve of silicate perovskite has a small positive slope of 19.5 (±5.5) K/GPa. The melting point of (Mg_0.9Fe_0.1)SiO₃ perovskite is 3800 (±300) K at 96 GPa; by extrapolation to 136 GPa, it is 4500 (±500) K at the core‐mantle boundary. These values provide an upper limit to the geotherm through the solid mantle, and they are compatible with recent estimates of the temperature in the core being high (∼4500 K at the core‐mantle boundary). Our melting curve implies that the volume change on melting increases at 60 GPa from ΔV_m = 0.0 (±0.2) cm³/mole to ΔV_m ≅ 0.16 (±0.03) cm³/mole. We derive an equation of state for the melt from our data, and find that a highly coordinated structure is required to explain the molar volume of liquid (Mg,Fe)SiO₃ at pressures above ∼ 20 GPa.