Non-arc basalts of Archean and Proterozoic age have model primary magmas that exhibit mantle potential temperatures TP that increase from 1350 °C at the present to a maximum of ∼ 1500-1600 °C at 2.5-3.0 Ga. The overall trend of these temperatures converges smoothly to that of the present-day MORB source, supporting the interpretation that the non-arc basalts formed by the melting of hot ambient mantle, not mantle plumes, and that they can constrain the thermal history of the Earth. These petrological results are very similar to those predicted by thermal models characterized by a low Urey ratio and more sluggish mantle convection in the past. We infer that the mantle was warming in deep Archean-Hadean time because internal heating exceeded surface heat loss, and it has been cooling from 2.5 to 3.0 Ga to the present. Non-arc Precambrian basalts are likely to be similar to those that formed oceanic crust and erupted on continents. It is estimated that ∼ 25-35 km of oceanic crust formed in the ancient Earth by about 30% melting of hot ambient mantle. In contrast, komatiite parental magmas reveal TP that are higher than those of non-arc basalts, consistent with the hot plume model. However, the associated excess magmatism was minor and oceanic plateaus, if they existed, would have had subtle bathymetric variations, unlike those of Phanerozoic oceanic plateaus. Primary magmas of Precambrian ambient mantle had 18-24% MgO, and they left behind residues of harzburgite that are now found as xenoliths of cratonic mantle. We infer that primary basaltic partial melts having 10-13% MgO are a feature of Phanerozoic magmatism, not of the early Earth, which may be why modern-day analogs of oceanic crust have not been reported in Archean greenstone belts.