The issue is that with time (usually about 6 months, depending on the thermal paste originally used by the manufacturer) the thermal paste dries up with use (much shorter time especially with heavy use - gaming, graphics heavy work, etc.). As the thermal paste dries up, the thermal contact between your IC (CPU/GPU) and heat sink is reduced or even lost. As this happens, your GPU heats up really fast (Your GPU runs on average about 35-40 degrees, but when you task it, it can go up really fast usually to greater than 100 degrees, if you don't have a way to cool it. The GPU is stable up to about 90-95 degrees, after which it will start to throttle its speed so that the heat reduces. If the cooling is done correctly, the temperature should stay at around 85-90 degree mark. The cooler it can run, the better performance it will give. (Do remember, the same issue can happen to the CPU as well, however the temperatures are slightly different.) If you said your computer shut off, then I would have suspected a faulty fan, however since the CPU seems fine, but the GPU has an issue, the most likely scenario is a dried up thermal paste, or an incorrect thermal paste application.
It is a good idea to replace the thermal compound every 6 months or so (For certain compounds like the IC Diamond, you will only need to re-apply every 12-24 months, as it doesn't dry up as fast).
Here's the plan of action I would suggest you take:
If you are comfortable opening and fixing your computer follow through, else take it to a qualified laptop technician in your area, and ask for a "thermal compound re-paste" done to your laptop. This should fix a lot of issues.
Caution: If you open your computer and do a thermal compound re-paste, you will void your warranty (if applicable)
Caution: You are advised to have a grounding strap attached to your wrist (or use a ESD safe glove) and use ESD safe tools, when working on your computer.
Caution: Repairing your computer is not fool-proof, and hence the following guide is given for your reference only. Please take extreme caution in repairing your computer. It can cause serious bodily injury and/or death.
- Precision Screwdrivers (Philips 00, 0, 1) (All of which should come in a cheap precision screwdriver set)
- Pry Tool
- Thermal Compound (Preferably IC Diamond or Artic Silver 5)
- Thermal Compound Cleaner (Preferably ArtiCleaner, else you can use Isopropyl Alcohol)
- Clean Tissue Paper
- Unplug your laptop, and remove the battery.
- Follow this video for dis-assembly: https://www.youtube....h?v=2UbT6o2AbZY
- Follow this video for removal of the heat sink and re-assembly of the heat sink: https://youtu.be/W9N0luaacPQ?t=575 (until time 17:00) (Please use this video only as a guide, and do not rely on it for re-pasting. Please follow instructions that come with your thermal compound to clean and apply the compound)
- Now would also be a good time to clean your fan thoroughly.
- Make sure to follow instruction that come with your thermal compound (Not the way that above video shows application of the thermal paste)
- Follow this video for assembly of your laptop: https://www.youtube....h?v=KyTbmyyEuDM
Please let us know what you do and how it went, whether for good or for bad.