Room size should have no effect on whether the sauna stove is hot enough, but it certainly has an effect on whether the room is hot enough for a decent sauna (and that depends on how much heat the stove has produced over time, as well as how leaky the sauna is, plus, of course, the volume of air to heat up).
In the game all that is guesswork, but, as JP_Finn said, in real life it's rather obvious as you can feel it immediately.