Personally, I think it would just be too finicky, so I wouldn't allow it. There's also a lot of questions to it, is Heat Metal hot enough? Does the cooling instantly quench the metal? If these are true, why does Heat Metal not ruin the temperament of everything you use it on?
That said, spellcasters can definitely start a fire, and your smithing PC almost certainly will have knowledge of how to craft a sufficiently hot fire.
Spellcasters still have plenty they could do to help regardless.