Does high heat paint have to be cured?/painting around an inset stove

Supercell

I'm painting the surround of my inset stove and its mostly metal. While the area immediately beside the stove may get fairly hot (i doubt if its over 250C though) about 10cm away from it is hand hot but nowhere near the 250C these stove paints say they need to get to for 45 mins to fully cure. Does it matter in the long run if it never gets that high further away from the stove or will it peel away in time as a result?

I used a stove spray on it yesterday and made a balls of the job and don't want to go that route again:

I was thinking of using the stuff below on the metal area outside the brass arch, and using brush on stove paint inside it, the square but around the inset stove is the only bit that gets mad hot and the finish is fine on that so not going to bother with it.

https://www.rustins.ltd/rustins/our-products/speciality-paints/quick-dry-heat-resistant-black-paint

Would I be better off getting a black radiator paint instead? All suggestions welcome!