Ford - Explorer :: Subtle Whining Sound Coming Somewhere From Outside The Car

A few days ago I was driving on the freeway for about 20 minutes and started hearing a subtle whining sound coming somewhere from outside the car. To quickly narrow it down to the engine, a wheel or the drive train, I pushed the clutch in, took it out of 5th and waited for the RPMs to drop. Then I hit some noisy rough asphalt and couldn't tell. Oh, well.

Here's the first big clue. When I shifted back into 5th, the gear shifter went into gear with no problem, but the clutch would not re-engage despite the pedal returning to its normal position.

Here's the second clue. Since I couldn't get the clutch to re-engage I decided to try one more data-gathering action. I turned the engine off (still coasting at 70 mph) and tried to restart. It would not restart, exactly as if I had not depressed the clutch pedal. So, I coasted for as long as I could and then walked the remaining 1.5 miles.

Here's the third clue. When I got back to my car about an hour later I tried to start it again. No joy, but then I heard a click underneath the car when I released the clutch pedal. I tried once again and it started. I drove the remaining 1.5 miles to the exit and started to notice the clutch appearing to stick for a second and then suddenly release. When I got to the gas station where I was before, it was done, just like on the freeway. Again, the gear shifter and the clutch pedal operated totally fine, but it seemed that the business end of the clutch would not re-engage until it cooled off. After it cools off, everything seems to work just fine.

So:

1999 Explorer Sport
4L V6 SOHV
5-speed manual
196,000 miles

What should I check?