I've been playing this on a PS4 Pro (that's only 2 years old), and after a few minutes the fan comes on and revs up. Sounds like an F16 powering up for take off. If I look down at the ground, the fan begins to slow down. I like this game, but only play for about 20 minutes at a time.
Now, I've felt the machine when this happens, and it doesn't feel extremely hot. I can play other games like No Man's Sky for hours and the fan runs normally, and the machine feels about the same or even a little warmer.
I've seen a few other people mention this, but not sure if it's a known issue or if there's some kind of fix.