Na the paint is fine. As long as you prep it as best you can, and give the paint every chance of sticking, it shouldn't lift off. If you are worried about the heat, use some VHT engine paint.
I don't think any brand of paint specifically, as long as it is black enamel, not acrylic I suppose. I just used a can I bought from Repco, can't remember the brand, but it is fine, and that has been 3 months since I did mine.
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