Great, we've got good information!
#1 - That power supply fan is certainly suspect.
Can you carefully blow the dust out with a vacuum cleaner on reverse?
Check out
http://www.ehow.com/tips_3664.html
and
http://www.ehow.com/how_3664_clean-c...s-insides.html
Make sure that you are well grounded, as static electricity ranks right up there with heat for killing PCS!
I'd first attack it from the outside vent (probably in the back). Then I'd power up and see if the power supply's fan noise had changed. If it hadn't I'd take the cover off and CAREFULLY blow the dust out. If there is a lot of dust, you may want to do this outside.
It is possible that the power supply will need to be replaced, but first lets try this:
# 2 - Your motherboard should have temperature and fan sensors. We need to see how hot it is in there, and also if any fans are failing.
If you have a utility installed for this purpose, then go ahead and use it. If not, you can download and install Intel's active monitor from:
http://support.intel.com/design/motherbd/active.htm
I don't have an Intel motherboard, so I can't test it. If the application is able to keep logs, go ahead and let us see a few hours worth of them. If not, just keep a notepad handy and write down some history. If you can, start from the cooled off state.
If I were to place a bet, I'd expect one or more temperature zones to gradually increase over time.
Let us know what happens!
Also, my comment about the case cover wasn't meant to discourage you from going into your computer. I meant that you don't want to do what I've sometimes done and LEAVE THE CASE OPEN for weeks at a time. That will disrupt the airflow!
Have fun,
Guy