Is that 200C or 200F? Whatever, personally I'd use a wall-wart to power the project at, say, 12V for safety and ease of control. Mains voltage + steel box would worry me.
You might have difficulty finding mains cord and cheap (i.e. plastic rather than ceramic) cord clamps, insulators etc to withstand the temperature, so it would be better IMO to have all the control electronics external to the box. As for heating 'coils', have you considered using standard high wattage resistors?