Bonjour Paul !
1. Il fait mal doesn't exist at all in this context The only meaning of the phrase on its own would be He hurts.
or Il fait mal [quelque chose] = He's doing [something] wrong.
2. Il ne fait pas chaud has indeed a similar meaning to il fait froid, i.e. It's not warm.Though the meaning is close, these are two different sentences, in French as in English.
I hope that's helpful!
Bonne journée !
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