Thank you for your answer.
I'm not sure at all that the temperature problems are in the GPU though. They could be from any number of reasons.
I have found another thing out. When the laptop goes down, it's not only the part at the back of the right fan exhaust that is glowing hot. It is also the area on the top right side of the keyboard, around the power button. I have installed a new SSD disk since the old one broke, maybe this could be the cause of the over heating. I need to investigate this further.
Regarding the RMA. ASUS in Sweden repaired the laptop this fall due to the 2 year factory warranty. I have a 3 year warranty still in effect but with the store where I bought the laptop, so according to the repair center in Sweden I need to contact the store, send the laptop there, which will send it to ASUS, which sends it back to the store, which sends it to me. Makes perfect sense doesn't it? Considering I have had many major faults with it since its purchase one would expect a more convenient method of repairs but no.
After talking with Dustin, where I purchased the laptop, they have informed me that even if the fault of overheating is caused by ASUS support (since the behaviour started to appear after I sent it to service there) I will have to pay the deductible of the insurance myself, since I purchased the laptop through a company where I was consulting.
Now I can see that bad things happen but I am not very happy with the way things have developped with my ASUS computer and ASUS support. Will ASUS support even manage to fix an error which is hard to repdorduce, the laptop only turns itself off maybe once a day, annoyingly enough though. Or will they mess it up even further again?