The two convective systems that dominate Earth’s internal dynamics meet at the boundary between the rocky mantle and metallic liquid core. Energy transfer between processes driving plate tectonics and the geodynamo is controlled by thermal conduction in the lowermost mantle (D′′). We use atomic scale simulations to determine the thermal conductivity of MgSiO3 perovskite and post-perovskite under D′′ conditions and probe how these two convective systems interact. We show that the thermal conductivity of post-perovskite (~12 W/mK) is 50% larger than that of perovskite under the same conditions (~8.5 W/mK) and is anisotropic, with conductivity along the a-axis being 40% higher than conductivity along the c-axis. This enhances the high heat flux into cold regions of D′′ where post-perovskite is stable, strengthening the feedback between convection in the core and mantle. Reminiscent of the situation in the lithosphere, there is potential for deformation induced texturing associated with mantle convection to modify how the mantle is heated from below. We test this by coupling our atomic scale results to models of texture in D′′ and suggest that anisotropic thermal conductivity may help to stabilise the roots of mantle plumes over their protracted lifetime.