Last year my X200 started to overheat when I stressed its CPU's. After various research I decided it was a hardware problem - even setting the fan in disengaged all the time did not help. It quickly went over 90°C and then shut off brutally from hardware protection circuitry. After such shutoff, you can't start the laptop (it's not even taking charge) until you have briefly removed power and battery.
Without much confidence it would help, I disassembled the thing enough to check the silicon paste between the CPU and the cooler. There was little paste at the CPU, and none at all at the other chip (GPU? I don't know). I put a generous dab of paste in both places and reassembled.
This completely solved the problem. I can now run at 100% CPU on both cores continously, and the temps hardly go over 60°C. What I can't understand is why I waited half a year before I tried this. It's much cooler at less load too, so fan noise is decreased.
I'm a semi professional but this was quite an easy job. All that is needed is a Phillips #0 screwdriver and the Hardware Maintenance manual. And the silicon paste of course.