The Earth’s mantle is characterised by large thermal heterogeneities associated with hot rising plumes and cold downwelling slabs. These lateral temperature variations in excess of 1000 K may have a crucial influence on the rheology of mantle rocks. Here we use a numerical multiscale model that allows us to make predictions from first principles with no adjustable parameters on the deformation of MgO under the extreme conditions of mantle pressure, temperature and strain rate, in order to investigate the sensitivity of mantle viscosity to the temperature heterogeneities inferred from a global high resolution mantle circulation model. Our results show that under the very low strain rates of the mantle, MgO deforms mostly at low stresses (few tens of MPa) in an athermal regime, where the deformation is insensitive to both temperature and strain rate, leading to a very weak phase throughout much of the upper half of the lower mantle. In its lower half, the weak phase gives way to high material strength with thermally activated viscosities in the cold downwelling slabs, while much of the hot upwelling flow remains in the athermal regime, resulting in large lateral variations in the inferred material strength of MgO. Our results suggest the presence of large lateral viscosity variations in the deepest parts of the lower mantle, associated in particular with the graveyard of old subducted oceanic lithosphere.