The amount of heat flowing from Earth's core critically determines the thermo-chemical evolution of both the core and the lower mantle. Consisting primarily of a polycrystalline aggregate of silicate perovskite and ferropericlase, the thermal boundary layer at the very base of Earth's lower mantle regulates the heat flow from the core, so that the thermal conductivity (k) of these mineral phases controls the amount of heat entering the lowermost mantle. Here we report measurements of the lattice thermal conductivity of pure, Al-, and Fe-bearing MgSiO(3) perovskite at 26 GPa up to 1,073 K, and of ferropericlase containing 0, 5, and 20% Fe, at 8 and 14 GPa up to 1,273 K. We find the incorporation of these elements in silicate perovskite and ferropericlase to result in a ∼50% decrease of lattice thermal conductivity relative to the end member compositions. A model of thermal conductivity constrained from our results indicates that a peridotitic mantle would have k = 9.1 ± 1.2 W/m K at the top of the thermal boundary layer and k = 8.4 ± 1.2 W/m K at its base. These values translate into a heat flux of 11.0 ± 1.4 terawatts (TW) from Earth's core, a range of values consistent with a variety of geophysical estimates.