My machine is a 13" MacBook Pro with retina display, running Sierra. When I record a screen (video with sound), the machine heats up rapidly (80 celsius in less than 1 minute of recoding).
That sounds reasonable especially if you're not in a cold environment. You're recording at a minimum of 240 million pixels per second internally (display resolution plus scaling, at 60fps) — that's going to be strenuous on the computer just like any heavy video processing workload. 80℃ is not out of the ordinary for any situation where you're taxing system resources.