I didn't do a complete disassembly, but I took the cover off and removed the video card, and right away I could see that the processor heat sink was covered in lint. Used a pick to get the lint out and hosed everything with compressed air. And yep, the system is dead silent again.
Look: if your computer sounds like a 747 on takeoff while you're looking at Facebook, it is just possible that its heat sinks need cleaning.
After removing approximately one cat's worth of lint from my computer, I buttoned it back up and it was nice and quiet again. I did the same cleaning on Mrs. Fungus' computer, but she had a lot less cruft in hers.
Might look into getting a bigger heat sink for mine. Her computer reports a CPU temp of 99° while mine reports a CPU temp of 122°. Biggest difference is that she's got a vertical heat sink with a big fan on it, right in the incoming air from the rear case fan, while mine has a short horizontal heat sink with a smaller fan. Mine's temp is not out of spec, but cooler is always better.
Well, that was my chore for the day, I guess.