question about noises under the hood just after shutdown

I have a 2005 Prius in generally good condition. Lately my car has been making an unusual noise, and I thought I'd ask the Internet what it might be before I try to face a mechanic.

First, some background: Sometimes when I park and shut off the car after having driven for ten minutes or so, I notice that something under the hood makes noise for a little while (maybe ten seconds? I haven't tried to time it)--most recently, I listened especially for this, and noticed that the sound actually began after I'd turned off the car, only to stop a little while later. Now, this isn't the problem that I'm concerned about--I don't care what my car does after I turn it off, as long as it's supposed to do it. But if somebody can tell me what this noise comes from, it would be helpful.

Given that background, here's the problem: Lately, this sound the car sometimes makes after shutdown has become... whiny. It'll start out sounding like a normal fan or motor or whatever, and then it'll suddenly become somewhat louder and much whinier, and then after a few seconds it'll turn back to the old sound. It goes back and forth like that until it stops. It sounds like maybe a belt is loose or a wheel needs lubrication or something like that. Can anybody suggest what the problem might be, and how worried I should be about it?