Why didn't they...
Break the thermostat? There's no such thing as a heating control system that says "Oh, there's no thermostat attached, I better switch on 100% heat!!" No signal = no functionality one way or the other. That would have been the easy way out.
Plus, when they decided to break the window, the guy knew that would make the heater run continuously due to the cool air tricking the thermostat. So at THAT point they could have tried disconnecting the thermostat with nothing to lose.
I enjoyed the movie though. It reminds me of Open Water and Open Water 2. One bad decision or moment of bad luck and a seemingly innocent situation turns deadly.