Isn't this well known?
From "The seven ages of a planet," 1975, William M. Kaula (1926-2000), Australian-born American geophysicist and professor at the University of California, Los Angeles.
On the basis of almost universally held assumptions concerning the formation of the planets and the isolation of the solar system from outside influences it follows rather plausibly that all terrestrial planets pass in principle through seven stages. The processes involved include the solidification of grains from gas in the condensation stage, planetesimal interactions, and formation processes. Vigorous convection processes lead to the gravitational separation of iron and the outgassing of oceans. Other stages are related to plate tectonics and terminal volcanism. The ultimate stage of quiescence is characterized by a thick lithosphere and no volcanism.
If only leftists would go into an "ultimate stage of quiescence." But I don't think the universe will last long enough for that to happen.
There have been a lot of refinements since 1975 but, the Hadean period and the great bombardmenr, while difficult to document due the scarcity of geological evidence, goes to your point. However the discoveries in plate tectonics and greater understanding of relationships among the core, mantle and crust have revised our understanding of when and how the cooling will progress. In short, there are plenty of processes keeping the heat on. Without them, we would already be like Mars. Studies like this go back a couple of billion years and find incremental changes.