My MSI turns off automatically

I am having some problems with the MSI of my signature. It has always worked flawessly on top of a Zalman ZM-NC1000 and without the rear cover, but recently it has started to turn off itself after some minutes of gaming. I can understand it gets too hot but the interesting thing is that if I run Prime95 or the stability test included in Aida64 it does the same, reaching temperatures of only 75 C.
I have tried undervolt, underclock, overclock, overvolt, disabling and enabling cpu throttling and the result is always the same.
When undervolt, it might happen that the voltage is too low, but I think it should throw a BSOD in this case, not to turn itself off. Am I right?
I've been thinking about a lack of power supply since both the CPU and GPU take more power than the default parts that the laptop came with. However, it has worked fine until now so I don't see the reason... The charger doesn't get too hot when this happens and also the GPU is idling while running the CPU tests so power consuption can not be too extreme...
Computer works fine in overall except for that but I can't figure out what's the reason behind this problem. If it was overheat, why does it turn off when reaching temperatures of only 75 or even 70C? If it was lack of power, why does it happen when stressing only the CPU?

Any help will be appreciated. Thanks!

Edit: I just made a 3D render with Keyshot 3 (4 cores at 100% load for many minutes). The cpu reached a temperature of 89 C and it was 100% rock stable...

 

Nevermind, went back to my 9800 and everything is fine with minimum performance loss (bios clocked to GTS speeds).