The temperatures are getting down low enough I'm getting the whine again. The next morning it happens, I'll start with checking the fans to figure out which one it is.
How old are the fans and power supplies? The bearings in the fans do not have an infinite life. I've had to replace them in the past; it's a cheap and easy DIY replacement.
I bought the machine and video card new 3 years, 2 months ago. The machine is HP, and I bought a better video card separately and put it in myself. I found the noise -- it is the fan on the video card (NVidia GeForce 9400 GT). Stopping that fan stopped the noise. Also, the CPU and chassis fans spin vertically, they don't make any noise; the video card fan spins flat or horizontally, and it makes the noise. I'll take the next step with the fan viscosity or the ball bearings, and follow up with how it worked out.