Initiation of clement surface conditions on the earliest Earth

In the beginning the surface of the Earth was extremely hot, because the Earth as we know it is the product of a collision between two planets, a collision that also created the Moon. Most of the heat within the very young Earth was lost quickly to space while the surface was still quite hot. As it cooled, the Earth's surface passed monotonically through every temperature regime between silicate vapor to liquid water and perhaps even to ice, eventually reaching an equilibrium with sunlight. Inevitably the surface passed through a time when the temperature was around 100 degrees C at which modern thermophile organisms live. How long this warm epoch lasted depends on how long a thick greenhouse atmosphere can be maintained by heat flow from the Earth's interior, either directly as a supplement to insolation, or indirectly through its influence on the nascent carbonate cycle. In both cases, the duration of the warm epoch would have been controlled by processes within the Earth's interior where buffering by surface conditions played little part. A potentially evolutionarily significant warm period of between 10(5) and 10(7) years seems likely, which nonetheless was brief compared to the vast expanse of geological time.