Go to a hardware store and get a ScotchBrite Pad for the gridle. (One WITHOUT soap!)
For the body just get some 120 grit sandpaper and sand out the rust. Then repaint the section with High temp stove paint.

Great thanks, I'll give it a try.

A can of Diet Coke also works well with the Scotch Brite pad.

The acid in the soda does a good job of removing rust, and the diet soda doesn't leave a sticky residue that needs to be removed.