Do you have a RE Circulation button ?
pickup truck with a Arrow, below the A/C button ?
If you do, press that button.
It cuts off the Outside Air Flow, then the cooled air is cycled again & again
If that does not change anything, or at least not much...
Remove your Lower Glove Compartment Door & check the 2 electric actuator, just to the left of the Blower.
Watch this video:
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Right off from the Start, you would want to remove the glove box door , THEN operate the Climate controls, to see if the Actuator moves that White Lever.
If it does, then the Actuator is still good, but remove it & do what he does with the White Lever &
listen to the sound, like in the video, if you hear that noise, you will also feel a weight, that will be the door inside moving.
If you should need an actuator, there are 4 actuators in most Rams. all 4 are the same part number.
The very best actuators are the OEM Actuators.
After market actuators mechanisms can break easily
IF, you take off the UPPER Glove Compartment door ..
Look above the glove compartment itself & you will see another Actuator, it lets in or closes off Fresh Air From Outside.
I don't think that is your issue, just good to know.
View attachment 546732
The Last 2 Actuators, require that Center Stack, which is the part above, be removed & below that, there are some ash trays or cup holders . Behind that mess the Actuators there control the Mode 1 & Mode 2 Doors.
They control air going to the floor & defrost & dash vents
There are videos showing access to them