How to change the passenger side air vent, is it necessary to remove entire dash?

Douglass, Your A/C may have lost it's programming, blend door actuator could be faulty or A/C could be low on refrigerant. You may have to take in and have a good Tech. diagnose and estimate repair.
Check the attached links,instruction and guides, Good luck
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Dual climate controls drivers side hot passengers side cold have 2004...
hot on driver side
Drivers side vents will blow hot air while is turned on but passenger side...

they usually just need levering out , get a piece of cloth or similar to protect the dash then work around vent with a mid size flat blade screwdriver and out it comes

There's a small motorized flap that's controlled by the heating and ac system that's gone bad. This part changes the air to flow from the ac or heating side depending on settings. I had a 1999 Jeep Grand Cherokee with the same issue, the fix is relatively simple once you get to it, however you must completely remove the dash to get to the part. The part is about 15.00. When removing the Dash you MUST disable the air bags, if you do not you risk injury or death if they are accidentally deployed.

1-Remove the vent/radio housing.
2-Remove the cover panels on either side of the dash that get cover when the door is closed.
3-Remove the panel under the steering wheel.
4- Remove glove box to open space inside of dash.
5-Remove four bolts and connector holding passenger side airbag and remove carefully.
6-Remove cover plate over shifter.
7-Remove the center console.(2 bolts under armrest and 4 screws-2 on either side of the console)
8-Disconnect the wiring harnesses on either side of dash.(White and black connectors. 2 on driver 1 on passenger.
9-Remove the four bolts holding the center of the dash to the floor.
10- remove two bolts on drivers side dash where cover was and same on passenger side.
11- Unbolt the steering column ( 2 bolts under the wheel) and let it rest on floor.
12- The entire dash will remove from the car as 1 piece and each component can be taken out from there.

It isn't worth it to fish for the bolts from the inside. Take the support bar out and work on it outside the car. much faster.

It seems confusing, but easy if you take your time

Most unfortunately, the blend door mixing warm & Cold air in the heater plenum has broken on the right side. This is a somewhat common problem in Jeeps with left & right controls and it is necessary to remove the entire dash to fix this. Jeep has an updated repair kit.

It is a known problem with the WJ. And it require to pull the entire dash board out and replace the vent gate.

Navigation has no relevence at all. but what does is the vent system in the dash.there is a flap inside the vents under the dash it sounds like it is not moving on the passengers side.

You may have clogged vents. Is their alot of junk on the floor tword the engine bay. This could be clogging the inlet to the vent.

Another issue could be internal a clog down inside of the dash vent systems or you could have vent door operating issues.

Almost certainly blend motor failure. The heater matrix has several blend motors which divert hot or cold air the vents you select. The problem is, the buggers fail. Their £200 each and a nightmare to get to. Unless you actually want to remove your entire dash i suggest you put up with it. I understand a garage will charge about £1500.

Air doors behind dash are damaged and no longer function. Common problem with Jeeps. Removal of entire dash to repair.