I had a similar but worse problem. My cpu would run at 135 degrees Celsius when IDLE. Then a simple usage of the CPU would cause the temperature to spike above 220 again Celsius and the computer would just turn off.
I took off the back panel (the largest one with a semicircle out-dentation) and where the strongest fan air is coming out and it turned out my CPU had absolutely no thermal paste left. I don't know whether this is the same problem that you are having but I cleaned my cooling fan and cleaned the die on the GPU and CPU and the respective copper heat sinks, reapplied new thermal compound and the commputer is running at 90 at Idle (which I have no idea whether this is where it should be, but 45 degrees cooler than it was).