Instead of defervescere, I´d use rather exstinguere (to switch off), that is first choice in this situation. But if it is not an imperative, but an adjective, your second version is good. A variant is "frigidus ignis in corde" - just for the sound, the meaning is quite the same.
I still like defervescere. It actually has the sense of cooling off or calming down, while exstinguere is more like putting the fire out entirely, which I don't feel quite captures the meaning of a sentence like "cool the fire of your heart." IDK.
As you wish. Probably, you are an English native speaker. I´m not. Anyway, ignis frigidus is in fact a figure, oxymoron. Frigor is temperature below zero. So I got the impression that there is no fire at all in the end of the process.
I'm sorry, but frigus can mean anything from "a chill" to literally freezing temperatures, the former meaning is not metaphor, and frigidus allows for a similar range of meaning. What you suggested is like saying that in English, "cold" is defined as "freezing" and that if you say it's cold when it's 35 degrees F you're speaking metaphorically.
It is possible that I am misunderstanding the English word "coolness", then. Still, frigidus ignis is a figure, an oxymoron. I don´t say I don´t like it. I just felt a gap between the original and the translation. I said I did not want to argue and I meant it.
Yes, "frigidus ignis" is a figure of speech. So is "cool fire," the phrase the OP wanted translated - it is an oxymoron in both Latin and English. Not really seeing where the problem is since oxymoron is a literary figure of speech that writers have been known to employ intentionally, both in Latin and in English.
Can you think of a better word for "cool," one that you feel would make for a closer translation? No argument intended. This is meant to help the OP find a suitable translation for their sentence.
Maybe not better, but perhaps quietus, placatus. Quietus will make the same figure as frigidus, both are transferable to their words: quiescas / places ignem in corde (tuo). Frigescas ignem... is a bit too weird for me. Not impossible, though, but I miss the hint on apathia (in stoic sense) I feel in "cool". Still, I like the picture of freezing fire - ignis frigidus.