Re: calm down and cool down
I agree that "cool down" applies to anger, but I would never tell someone who was very sad to "calm down."
In fact, I really suggest never telling anyone to cool down or calm down. Being told to calm down when I"m not angry in the first place is pretty much guaranteed to make me become angry!
I know that wasn't your question, though. For you original question, I agree with ems.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.