No, they now do a lot of processing for each individual frame (and imagine doing that for 60 frames per second).

Thermally, mobile phones are not rated or designed for constant work. They want to do stuff only like 1 out of every 10 seconds and are designed to dissipate heat that way. At least the way I understand it. Even if there was nothing being done to the raw frames from the sensor, which hasn't been the case for a while, it's likely the processor would have to do other stuff to manage the resources.