Did you blow out the dust yet? Use short bursts of compressed or canned air.

Overheating is a definite possibility, and you have had your system long enough to consider a compressed gas blow out where you open the laptop and blow compressed gas from the inside to the outside through the fan exhausts to remove built up dust, or possibly even a repaste. However, especially as a gamer, it is in your best interest to run a utility such as SpeedFan or HWInfo to montor your CPU and GPU temps. This would confirm overheating as the cause in your case.

My suspicion is the BIOS update is NOT responsible for the overheating, but that you were on the margin of shutdown and just happened to cross over that margin shortly after the flash.

Dust is one of the most common causes of overheating, particularly on older systems where dust removal maintenance has not been done.