Not sure it would help if discolored with heat, but "Barkeepers Friend" is a cleaning product I use on stainless steel.
Its available at most supermarkets for around £2 -£3. Its non-abrasive but really effortlessly cleans well.
You can also try bicarbonate of soda - tsp of bicarb & drop of water to form a paste and just rub around the stained area.