I also think its a thermal issue. Invest in some Arctic Silver 5, but alot of people know, but for the record, its a very quality thermal compound that goes in between the CPU and heatsink. This stuff is what conducts the heat between the CPU and heatsink. If your trying different ways to cool the computer, and the timings of the beeping is changing, then it is indeed a thermal issue. If you can't figure this problem out with a new fan or compound, I suggest getting a new computer tower with better cooling. Or if you want to go all out, invest in water cooling.
"Just because I'm sitting between you idiots doesn't mean I want to go skiing!"