Interesting concept, it would be worth spending more time on it after the Jam ^^
The timer was way too fast to my taste because even moving between small rooms in the tutorial would make me reach max heat. Also, it would be nicer to the player if you pause the game/timer during the tutorial so that we can read the text without worrying about the timer.
A bit more feedback on the heat could be nice as well, for example, sound effect when you are heating a bit too much.