I worked at a joint that sold 360s. The ‘towelling’ was a real thing. Apparently they used crappy solder, which when combined with inefficient components and poor cooling, caused the GPU to develop dry joints. Wrapping it in a towel and turning it on would get it hot enough to cause the solder to melt again, and reflow the joints.

At least, that was the story going around at the time. Whatever the real cause, it often worked. That hardware was such utter dogshit, I’m still amazed that the brand survived. They must have lost so much money in that debacle.