A friend of mine is thinking about getting tropical fish for his cold water (50g), he has no heater and the temp is 20-21C. I tried to tell him but it didnt help.
Put simply it will kill them. The stress of changing rapidly will do the first bit of harm, then the lack of heat will slow their metabolisms until their organs cease functioning and they'll die.
He was going for a bronze cory (just one, arnt they supposed to be in groups?). He currently has a couple of goldfish, blackmoors, hillstream loach, wcmms.