What if they used a different medium, do you remember the solder iron sold on TV infomercials, battery operated, instant heat, melts solder?
The tip was made out of a novel type of silicon that multiplies temperature. If you put that between the layers of the chips and apply cold temps, which would be multiplied by 10, you could get an effective thermoregulator.
Law of conservation of energy says "NO". temp is merely a measure of thermal energy. You can't multiply energy. That would imply you created energy from nothing.