"I have taken it into Apple 5 times now and each time they refuse to find the problem."
They flatly refuse even to try?
If a machine is making a grinding noise and overheating to the extent that you say, it's pretty obvious that something is wrong. Has it made the noise when in the Apple store? If it has, I'm astonished to hear that the people there refuse to investigate.
When did you buy this machine -presumably you've had it from new?
When did the fault first become apparent?