Let's assume that the water, teapot and air are each a single temperature, but the temperatures may be different. The water cools by passing heat through the material of the teapot and then into the air. But, heat always flows from warm locations to cold locations, so for the heat to move from water to teapot to air, the first must be warmer than the second, which in turn must be warmer than the third.
If you let the temperatures in each material vary, then it's possible that this could be violated in specific, small locations (e.g. driven by falling, cooled water), but on the whole the answer will be the same.
Edit: another way to look at this is think of the initial condition, with the water hotter than the teapot, and the teapot being warmed by the water. For the teapot to get warmer, or the water to get colder, heat must transfer from the water to the teapot. But, as the temperatures get closer and closer, the heat transfer gets proportionally less and less (ignoring convection), with the heat transfer approaching zero as the temperature difference approaches zero.
A better physicist than I could prove that the temperatures will never match. However, even ignoring that, you can show that the temperatures will never pass each other. Let's say there is a moment when the temperatures are equal; the heat flow at that point will be zero, so the water cannot heat the teapot any further, and the teapot cannot cool the water any further.