download a program like speccy or hwmonitor and check the temperature of CPU and GPU when you're playing a game. If it climbs above 85C it's most likely overheating.
In view that you're crashing, make sure to enable logging to file or similar (which ever option is available in the program that you download) that way when the computer crashes you'll at least be able to go back and check what temperature was when it crashed.
Alternatively, write down the error code the blue screen gives you, that will give you some clue as to what caused the problem and possible solutions.
Upgrading GPU drivers is tricky on laptop with integrated and dedicated graphics as you need to make sure to update both. Not just dedicated GPU driver.