If the black is from the spray coating, ammonia or steel wool will remove it fairly well.
If, however, the discoloration is from actually overheating the stainless steel, the dark color is often "all the way through", and is permanent. But, being optimistic, it may just be surface oxidation. If so, try 100 or finer grit emery cloth. If you see a silvery color, then continue, using ever finer grades of emery cloth grit to give a clean, smooth luster when finished.
For the external copper, half a lemon used to scrub table salt on the surface works pretty darned well. Actually, any acid - except hydrochloric! (aka muriatic or "swimming pool acid" - it will permanently stain both stainless steel and chrome.)