Yup, that's hardware heating up. Either a processor overloading, a short circuit somewhere, or (again, most likely) a battery going bad. Most repair shops will be able to test out a spare battery and try to see if it doesn't heat up that way (or spot something glaring like a burnt element or something).
Has it gotten wet lately? That could also be a possible scenario and would explain why it won't boot and heats up (also probably means more extensive hardware damage, unfortunately).