The thermochemical boundary between Earth's core and mantle marks a profound change in composition, physical properties, and dynamics within the planet. The transfer of heat across this boundary represents up to a third of the Earth's surface heat flow Q surf (Lay et al., 2008). Convection in the mantle regulates the cooling of the planet, controlling the magnitude and spatial distribution of heat flow across the core-mantle boundary (CMB;Olson et al., 2015). The low-viscosity liquid outer core adjusts rapidly to changes in CMB heat flow (Jones, 2011), altering the power available to sustain the Earth's magnetic field (e.g., Nimmo, 2015a). Despite the importance of the CMB heat flow (hereafter called Q CMB ), there are large uncertainties on its present-day magnitude. Furthermore, recent upward revisions of the core thermal conductivity necessitate revisiting constraints on Q CMB (e.g., de Koker et al., 2012). To date, several approaches have been used to estimate Q CMB : petrological inferences on mantle potential temperature through time, simulations of Earth's magnetic field, and mantle convection simulations for different thermal gradients at the CMB. The allowable range of Q CMB is large when each approach is considered in isolation. By combining these approaches in a self-consistent way, we can better constrain the range of heat flow into the mantle from the core.To start, petrological observations of igneous rocks at the planet's surface point to trends in the melting conditions over geological time, and are used to establish rates of mantle cooling (Herzberg et al., 2010). A present-day cooling rate is combined with inventories of radiogenic elements in the mantle and crust to infer the Q CMB needed to account for the mantle heat budget for the present-day Q surf of ∼46 TW (Jaupart et al., 2015). Based on petrological arguments (discussed further in Section 2), Q CMB estimates fall in the range of 14-20 TW for a nominal Urey ratio of 0.3 and secular cooling rate of the mantle of 50-100 K/Ga (Herzberg et al., 2010;Korenaga & Karato, 2008).Several authors have investigated the Q CMB needed to account for the strength and morphology of the Earth's magnetic field. The upward revision of thermal conductivity in the liquid outer core (de Koker et al.