The distribution of geochemical species in the Earth's interior is largely controlled by fractional melting and crystallization processes that are intimately linked to the thermal state and evolution of the mantle. The existence of patches of dense partial melt at the base of the Earth's mantle, together with estimates of melting temperatures for deep mantle phases and the amount of cooling of the underlying core required to maintain a geodynamo throughout much of the Earth's history, suggest that more extensive deep melting occurred in the past. Here we show that a stable layer of dense melt formed at the base of the mantle early in the Earth's history would have undergone slow fractional crystallization, and would be an ideal candidate for an unsampled geochemical reservoir hosting a variety of incompatible species (most notably the missing budget of heat-producing elements) for an initial basal magma ocean thickness of about 1,000 km. Differences in 142Nd/144Nd ratios between chondrites and terrestrial rocks can be explained by fractional crystallization with a decay timescale of the order of 1 Gyr. These combined constraints yield thermal evolution models in which radiogenic heat production and latent heat exchange prevent early cooling of the core and possibly delay the onset of the geodynamo to 3.4-4 Gyr ago.