For gaming, it ain't getting hot unless you do something STUPID like pick some power-hungry GPU.
For gaming with decent graphics at a decent (i.e. 30+) framerate, yes, it's gonna put out a lot of heat. You're looking at a 980 ti or Fury X to handle 4k, which means a total system power (under load) of ~400 watts. If you want actually goodgraphics, you need SLI/Crossfire, which means ~700 watts or more. That's quite a lot of heat.
Now, if you only want to browse the web or watch a movie, sure, even a low-level low power PC can do that. Hell, my eee901 netbook with it's super-shitty integrated Intel graphics could push 1920x1080. But, we're talking about gaming here, and that takes vastly more power.