Constant, loud, Buzzer

I think I may know they answer to this question but I really need to know how to fix it. I have a new 20" Cinema Display hooked up to a Powermac G5. The problems is after alot of use my computer will start to emit a very loud, constant, buzzer. I think this is due to the fact that the Cinema display is becoming to hot? To turn off the buzzer all I have to do is turn down the brightness on my monitor, or just turn the monitor completely off. Hence the reason I think the buzzer is due to the monitor. Is there anyway to fix this problem, or do I just need to keep my monitor brightness down? And yes I do turn the monitor off when not in use.