"cooler colors seem farther away" strikes me as a classic "rule" of the sort that's simply wrong. I mean, there *might* be a paper somewhere that outlines a careful study, but I have not seen it, and it doesn't pop up on google, and I have mislaid my copy of Arnheim.
It's probably a bastardization of the methods used to paint things which are distant, which more resemble desaturation, or reduced vibrancy, but which are not quite that. It strikes me as similar to the way you make audio sound distant by boosting the mids. With the brush, you just have to feel it, in the end, although to be sure your teacher can give you some suggestions.
Properly filed away, this "cooler colors" sort of thing could be useful, as a property of a picture it's something to note, something to think about (see post #19).
If you file it, rather, as a rule, and attempt to make pictures by directly applying the rule as a method, an algorithm, you're going to tend to focus on whether you have the background cool and the foreground warm, rather than focusing on the actual question which is "does the background look farther away."
It is absurdly common to run in to people who will, when you say the equivalent of "this looks X" will cite a rule and say "no, I did Y which produces the opposite of that effect, so you are wrong" which is extremely weird. They're been distracted from the things that are in front of them by the procedure they are following. They're mixing up a batch of muffins, and refuse to taste them to see if they forgot the salt no matter how often you say "there's no salt in these, they kind of suck."