Most powder coat places also do ceramic powdercoat which we used for the exhaust header on our racecar. Looks great and handles the heat perfectly as well as impact.
Find a local place and drop it off, its not too expensive and may be even cheaper if you choose a popular color.
High heat paint
will change color around the burner hole and fade outward a little ways. it should be pretty stable further out. Heck you might like the effect! The range hood should be just fine.
If your new color is compatible or a good contrast,you might mask it around the burner about maybe 1-1/2". Not sure how that would work.
You could paint
it High heat black, then bake it, it would likely turn a pretty gray in the oven.
There are also home powdercoating kits available Look on You-Tube for several videos. (don't know about ceramic)
Not sure how regular powdercoat takes heat.