Although some video can certainly stress a system, what you're describing doesn't really have anything to do with video. Of course, I don't know much about sports but I do know about web design and computers. That being said, I've gone to the ESPN Fantasy Baseball site and there is nothing there that would cause a GPU issue. When you say your computer is "beeping", is it coming from the tower itself or from your speakers?
Looking at your specs I don't see any reason you should be having any issues graphically. As a side note, if you are/were experiencing overheating issues your machine would either fritz out (anomalies or artifacts on your screen) or it would shut itself down. There are safeguards in place within the BIOS of each piece of hardware. A threshold if you will.
Sounds to me like the issue might lay somewhere else. First, let's find out where the beeping is actually coming from.