Just wanted to post my results/thoughts. Maybe it will help someone else.
My wife's car (2001 RX300) was making this annoying BUZZING/GRINDING sound. And there was no hot air.
To get to the servo:
1) Took off the bottom panel below the glove box.
2) Took off the 2 hex screws at the bottom and 2 screws at the top of the glove box.
3) Unfortunately, my glove box was tethered to the airbag cord. So I had to squeeze the tabs to release the small panel, pull it through, then rotate the panel to separate from the glove box. DO NOT UNPLUG THE CORD!!!!
4) Remove 3 screws on the white plastic "vent" on the left side.
5) Remove the panel below that (has a flat-head plastic screw/snap on it).
Trying to see if maybe the arm was just stuck:
Next, I detached the arm on the air mix servo from the other piece, and turned the air to HOT, then COLD, etc. The arm on the servo did NOT move. So, the other guy's suggestion wouldn't work for me. Although, his pics were GREAT!
So, I had to take the air mix servo out:
The bottom 2 screws weren't that bad. But that top screw behind the pipes was a PAIN IN THE BUTT!
I was able to get the screw partially out with a stubby screwdriver (#2 phillips). But then I had to use a small ratchet with a #1 phillips attached. Both were at an angle. And wow, what a pain. Maybe the 2001 model is a little harder than others? It wasn't easy.
Then I just detached the servo cable.
Here's a pic of the servo out with the ratchet that I used to get that screw the rest of the way out:
Then, I took the servo apart. Turns out I had the same issue where the motor was becoming separated from the worm gear.
You can see that here:
So, I just used a gear puller (I had bought one a couple of years ago to fix the actuator for the door lock), to pull the "key" down the shaft a little bit. I'd guess about 1/8th of an inch?
Here's what the gear puller looks like:
Once I pulled the "key" out, there's very little gap anymore. So, it's not going to come loose again.
Here's a pic of the fixed servo:
Notice the extra space between the motor and the key after if was fixed (sorry that the angles were different).
Anyway, I didn't try to clean any contacts, or add any grease or anything like that. Just fixed the gear/key gap.
Everything works now. Servo arm moves all the way up (HOT) and all the way down (COLD). And the NOISE IS GONE.
Thanks to everyone for the info!