Nice game. Would have been good to have a CPU player, and I don't really see the significance of the cold timer if you can just mash the spacebar to stop it.
As others have mentioned, would be nice to have some simple sound effects, doesn't even need music.
I also didn't see the screen transition requirement, but if I'm honest I stopped after 3 levels because all the levels were the same and it felt like a grind to find the door.