SUMMARY Heat transfer through Earth's mantle is sensitive to mantle thermal conductivity and its variations. Thermal conductivities of lower mantle minerals, bridgmanite (Bm) and ferropericlase (Fp), depend on pressure, temperature, and composition. Because temperature and composition are expected to strongly vary in the deep mantle, thermal conductivity may also vary laterally. Here, we compile self-consistent data on lattice thermal conductivities of Bm and Fp at high pressure to model lower mantle thermal conductivity and map its possible lateral variations. Importantly, our data set allows us to quantify the influence of iron content on mantle conductivity. At the bottom of the mantle, the thermal conductivity for a pyrolitic mantle calculated along an adiabat with potential temperature 2000 K is equal 8.6 W m–1 K–1. Using 3-D thermochemical models from probabilistic tomography, which include variations in temperature, iron content, and bridgmanite fraction, we then calculate possible maps of conductivity anomalies at the bottom of the mantle. In regions known as low shear-wave velocity provinces, thermal conductivity is reduced by up to 26 per cent compared to average mantle, which may impact mantle dynamics in these regions. A simple analysis of threshold and saturation effects related to the iron content shows that our estimates of thermal conductivity may be considered as upper bounds. Quantifying these effects more precisely however requires additional mineral physics measurements. Finally, we estimate variations in core–mantle boundary heat flux, and find that that these variations are dominated by lateral temperature anomalies and are only partly affected by changes in thermal conductivity.