If you do decide to use Arctic Silver 5 or similar then double check that there's no electrical components near the heatsink. With it being electrically conductive there's a risk of shorting. MX-2, 3 or 4 are safer (and better) however they're designed to work best under pressure (about 40lbs per square inch, I think).
It may not actually be a heating problem. Some laptops like the IBM T4n series use a BGA Graphics chip that are well known for problems like this. Basically the problem is this: The BGA stands for Ball Grid Array and instead of having pins that are pushed through holes and soldered at the back of the motherboard = quite a solid method, the BGA chip has tiny little balls where the pins would be and the mobo has little cups that they rest in. There is a tiny bit of solder between the balls and cups that both hold the chip in place and help complete the circuit. What sometimes happens is that with the constant heating and cooling thermal stress (and any knocks) tends to cause cracking and 'DRY' joints that cease to conduct and the effect is what you see. Extra pressure on the chip by fitting an extra/thicker pad makes the contact again - until it eventually stops altogether. It is possible to "repair" the problem by carefully heating up the chip with a heat gun until the solder melts and the joints are repaired, but it is quite a complicated procedure and requires the right equipment, and the temperatures and rate of temperature change is critical, but done correctly it has a near 100 percent success rate.