There was a time a few years back when several notebook computer manufacturers got burned by a faulty design of graphics chip (GPU). My wife suffered from problems because of it. The GPU from Nvidia allegedly ran far hotter that it was supposed to, so in the case of the wife's HP TX1000 laptop, the fans would run full blast all the time, but ultimately the thermal expansion/contraction of the GPU in relation to its ball grid array on the motherboard caused enough of the joints to fail at certain temperatures the machine would lock up. It would then refused to start up again until the temperature had lowered sufficiently, and presumably the contraction of components closed the fractures in the solder joints.
I wonder if you are suffering from a similar phenomenon?