I'd say its the driver side blend door actuator. If you have dual climate controls, you have 2 servos - one for the driver and one for the passenger.

Working on alot of mid 2000s GMs got me *very* familiar with actuator issues lol.

It could also be an issue with the hvac controls (parts manual calls them the "CONTROL HEAD") or their connectors, but I'd blame the actuators first. GM's servos were like $10 a piece, I'm sure chrysler is the same.

While you're in there, I would check for debris inside the ducting - I've seen cases where a pen or loose change fell in through the defrost vents and blocked a door.

Good news is I dont think you have to take the entire dash apart to get to it. I quickly googled a schematic for reference:

 

I’ll have to try that this weekend. Maybe keep my head on it while changing the temperature to see if I can feel it move or not.

 

Actually your heater core is half plugged up. WHat you should do is backflush the heater core and then reinstall the heater hoses to the heater core backwards. I had the same problem and i have been having heat on both sides for 5 years now.

 

I was gonna suggest the same thing. The heater in my 2002 1500 blows a little less than hot on the drivers side and cold on the passenger side. I've heard that filling it with CLR for a few hours and flushing it and back flushing it will solve the problem. I've flushed mine twice and it was very nasty the first time, then just dirty the second time so for the third time, I'll dump the CLR and then flush for a longer period of time in each hose.

And remember, not too much pressure. 16 psi will damage it severely or bust it.

 

I have the exact same issue with my 2016 Dodge Ram 3500, 6.7 Cummins 4x4. It does NOT have dual climate control but will blow cool air on the driver's side and hot on the passenger's. AC works fine all around and it switch from defrost to panel to floor just fine. The heat difference is the only problem. Did y'all ever figure out if it was the heater core or actuators?

 

www.blenddoorusa.com

This is a complete rebuild kit for 3rd Generation (02-09) Dodge Ram trucks to fix your heater and air conditioner.