High heat paint is fine, especially if there isn't much rust. Throw at least two coats on there to be sure. Regardless, I'd suggest taking a wire brush to the rust first to allow the paint to adhere better.
If you have a higher quality pit (with thicker walls, especially on the fire box) and the rust is significant, you can take a right-angle grinder with a braided-wire disc to take a majority of the rust off. Word of advice, wear old clothes and a face shield, b/c this is a dirty job if you go this route.
We had an old towable pit sand blasted and repainted recently. Looks like new. I'd only suggest that if the rust is very significant and the pit is large.
I'll try and figure out who it was, my dad hired them, they fixed and powder coated all of his wrought iron furniture that is 30 years old and while out there told him they could do the pit too, so he did it. It hasn't flaked or rusted and was done about 4-5 years ago.