The brown color is the natural tarnishing of copper. In time it will turn green. It can be removed simply by using a good copper polish. The copper polish may also remove the white and black discoloration around the hot spot.

Due to the brown color, it sounds like this hood was not given a protective finish at manufacture. However if it does have a plastic type protective finish, or if the protective finish has worn off in areas, you'll have to remove all of it in order for the polish to work. A paint remover will probably do it, but the fumes can be awful and you'll need to protect adjacent and lower surfaces from the drips/splatters. After you bring the surface back to an acceptable state, you can re-apply a protective finish, although I prefer leaving such surfaces unprotected and using regular polishing to keep them looking nice.