We address the first several hundred million years of Earth's history. The Moon-forming impact left Earth enveloped in a hot silicate atmosphere that cooled and condensed over ∼1,000 yrs. As it cooled the Earth degassed its volatiles into the atmosphere. It took another ∼2 Myrs for the magma ocean to freeze at the surface. The cooling rate was determined by atmospheric thermal blanketing. Tidal heating by the new Moon was a major energy source to the magma ocean. After the mantle solidified geothermal heat became climatologically insignificant, which allowed the steam atmosphere to condense, and left behind a ∼100 bar, ∼500 K CO2 atmosphere. Thereafter cooling was governed by how quickly CO2 was removed from the atmosphere. If subduction were efficient this could have taken as little as 10 million years. In this case the faint young Sun suggests that a lifeless Earth should have been cold and its oceans white with ice. But if carbonate subduction were inefficient the CO2 would have mostly stayed in the atmosphere, which would have kept the surface near ∼500 K for many tens of millions of years. Hydrous minerals are harder to subduct than carbonates and there is a good chance that the Hadean mantle was dry. Hadean heat flow was locally high enough to ensure that any ice cover would have been thin (<5 m) in places. Moreover hundreds or thousands of asteroid impacts would have been big enough to melt the ice triggering brief impact summers. We suggest that plate tectonics as it works now was inadequate to handle typical Hadean heat flows of 0.2–0.5 W/m2. In its place we hypothesize a convecting mantle capped by a ∼100 km deep basaltic mush that was relatively permeable to heat flow. Recycling and distillation of hydrous basalts produced granitic rocks very early, which is consistent with preserved >4 Ga detrital zircons. If carbonates in oceanic crust subducted as quickly as they formed, Earth could have been habitable as early as 10–20 Myrs after the Moon-forming impact.