|If you eventually are able to enter the bios, check the temperature limits that are set. It might be like Othehill mentioned earlier, that they are set too low.|
It does sound like heat is the problem, but the beeps can also be caused by voltages that are out of specs. It's not very likely in this case, but I mention it 'just in case'.
By the way, your comments about disabling the beeper completely puzzle me. I have never heard of such a thing.