It is not that the GPU is getting hot, when hot enough it is taking down the computer with it.
Just make sure your laptop has some space to get free air. Like putting a dvd case at the end of it, so the heat doesn't heat the surface beneath it, so the laptop needs even more cooling. My old laptop did shut down too at times and it helps to do like I just said.
Also, vacuming at the vents does help. I know it's not recommended, but I've done it like 100 times on that laptop, it's 5 years now and my brother are still gaming on it this very day. Just don't do it while it's on and remove the battery to make sure there is no electricity in it while doing so.