Edit: Heat released is also proportional to the temperature differential between the wire and the outside world, as well as a constant associated with how well

Edit: Heat released is also proportional to the temperature differential between the wire and the outside world, as well as a constant associated with how well it's thermally insulated. The wire temperature rises till either some sort of breakdown occurs or that rate of heat release balances the rate of heat production. The spirit of that original comment is correct, but this feels like a nuance that might matter to somebody new to the topic.