Here is the deal, I had the same problems playing gta v. The solution is downclocking the videocard's clock.
It didn't only improve power consumption but it also makes the game RUN WAY BETTER. I'm not using all the 4 GB because I don't want to stress the card as it get's too hot and I must run the fans at 80% of the speed in order to get it cooler, but I don't like the loud it makes, so i stay still up to 3GB. Anyways, everything is set up to ULTRA, besides the antialiasing which is at 2x.
The advanced graphics also are not set to maximum settings, i just turned on the "High quality shaders" or some stuff like that and the graphics are VERY REALISTIC and SMOOTHY. Playing online I sometimes notice the laggs but it is due to ping, cause when I play offline it is always smooth.
How to get the card work properly?
Download the TRI X software for overclocking: https://www.sapphireselectclub.com/ssc/TriXX/
Install the software.
Once installed, set the clock up to 900MHz or lower(until 800MHz it's ok).
Set the VDDC offset to 0mV, this will decrease the power consumption drastically and will make your card cooler(from 5 to 10 C° lower).
Now save your settings so the next time you will only have to load the profile you have created previously.
If you want this to be your permanent settings, you can set the software TRI XX Tweak to start with the Operative System and automatically load the profile by setting the data as you want it to be(you can make it run silently, thus in background, so you won't even notice it starting).
GOOD LUCK GUYS!!