Wood stoves have something called a baffle plate that redirects hot air so that it flows along the interior top of the unit before leaving through the chimney. The purpose is to heat the metal enough for radiation tranferrance. I often put a ceramic-coated cast iron kettle on top, and it will boil if left for a while. Anyone who sits on the stove would have a very bad time.

Built in fireplaces work differently but aren’t typically sit-onable.