this site has some simple observations and info you could use to help narrow the issue...

http://heatertreater.net/Ram%2002-08%20Listing.html

and another thread on the recirc door
https://dodgeforum.com/forum/3rd-gen...0-minutes.html

 

I had the crumbling forward dash & the grids for the AC/Heat vents fell down into the vents. I vacuumed some parts out, but not enough pieces to account for all the grids. I have weak heat. If I set them temp select **** to full heat with the blower off for a couple of minutes, then turn the blower on low setting I get good heat for 15 seconds & by 20 seconds it is neither hot nor cold. I could not locate a valve in the heater core lines coming off the engine block- my first suspect. Then I read about this "blend door". I am now suspecting my blend door is jammed with the broken grid plastic pieces. It looks like I can drop the blower motor, which might allow me to get my hand, or fingers, access to the blend door to pick out the rest of the plastic pieces. If the AC/Heat control module is the culprit, can I disconnect it via access from the blower motor hole. Then I can rig a simple "old school" cable/coat hanger control to select heat or AC. Even though I could blend this way, I don't need the blend feature because I still have blower speed control. I'm in Florida. If its not hot or cold out I don't need the Heat/AC system, I just open the windows (old school again).

 

You might also try removing the specific actuator motor and carefully hand operating the dampers you can reach. Its also possible that you have a bad actuator motor, although more likely, the blend door broke (way more common) which requires removal of all the dash components, and the hvac box to repair.