If you remove the actuator, you should be able to move the blend door by hand. Just turn the the piece that goes into the actuator. At east I could do that on my 99.

 

My 2000 Silverado never shuts off the heat with the control also. I have not tried anything other than bypassing the heater core at this time.

Not sure which part to blame, the control head, the actuator or the blend door - although the actuator being the moving part most used in the system would be the most suspect. I hear nothing when the dial is turned. A known good one would be nice to test with.

I'll be watching this thread with anticipation.

 

From my research, it's the actuator. I did a mess of reading the other day and that's my belief.

I have, and will try to post the links to the articles which led me to this conclusion. They are on my other computer and I am out of the country at this time.

Of if you like, simply Google "2001 Chevy Silverado heat will not shut off" and do some reading. I read every link on the first two pages and while some are just speculation, there are a few posted by trained mechanics and links to Chevy service bulletins which seem to point the dirty digit squarely at the actuator.

I need to rip my dash apart to install a new stereo so I will do that, the actuator and the cabin air filters all at the same time.

Get your google on and get your heater fixed. The actuator is cheap but the re-installation is a bit tricky. All the info is on the web.

Good luck.