“Heat rises” is a fairly common phrase but anyone who has ever soldered knows it’s false. Heat flows from hot areas to less hot areas.
“Hot air rises” is better than the shorter phrase because this is most often the case here on planet earth. However it is not always correct, if the surrounding air is also hot there is no movement.
The most accurate phrase to express this idea is, “heated air rises”. But that doesn’t roll off the tongue well, most people will never learn soldering, and when the surrounding air is the same temperature who cares, so “heat rises” will have to do. 🙂