How do you paint an old rusty wood burner?

You can purchase hi heat paint for cars, made for exhaust and hot parts, this is an option

If you put olive oil all over it, it will remove the rust and give it a nice darker finish. Put it on with a brush, and wipe off a lot of the rust. Will also help protect the finish. If you want to paint it, wash the loose rust and or oil off. I like rustoleum spray paints, they come in all kinds of colors and have a primer built in, makes it easy. If you go bright and don’t like it, you can always spray over it with a matallic gray or black paint. The textured paints hide a lot of the roughness of old metal esp in the flat finishes. Have fun with it!!!

I like the fun color idea. Wire brush off rust, prime with rust converter, spray paint with exterior Rustoleum paint

They make a product in automotive stores called naval jelly. It gets painted on to turn rust to be able to paint. I would take a wire brush to scrape or clean off as much rest as possible, try some corse steel wool? Remove as much as you can after the naval jelly ( follow the directions) spray paint. Use a Rust-Oleum paint.

I like the idea of leaving the rust but it might eventually rust through leaving holes. Painting with a product like ‘Rustoleum’ might be the way to go.