Even though you've already gotten it done, burn marks are quite similar to rust, as far as painting goes.
I usually start with a dark brown for burns-- one that's nearly black. Then I stipple it with a mix of the dark brown and a dark red (GW scab red isn't a bad shade for that). From there, it's just lining the area with various silvers so that it looks suitably charred, and maybe even a little warped. You just want to make sure the dark brown shows through a tiny bit around the inside of the barrel and the edges, and around any exhaust vents.