Well I can tell you if I set my Sapphire radeon Nitro fury card to a VSR of 4K
Then run Rise Tomb Raider, it forces the fans of my card to ramp up in speed Ghost.
And does much the same for every other game set with a VSR of 4K setting.
It does put more load on the card in respect to the Gpu processing power required.
Just out of intrest what sort of frame rate results are you getting from a RX 480 card at a VSR of 4k ?
I would like to do a comparison of it between the RX 480 and my Nitro Fury if you could post the FPS results.
And some in game graphical detail settings you are running.
PS: your card may run a bit hotter, I know mine does only a few Oc though.