Since this comes up with regularity, I tore apart my perfectly good interior to take photos.
1. Torx Bit & Driver — I think it's a T15 or T20. If you've bought a bit screwdriver in the past decade, you should have the one you need.
15 minutes, tops, if you've never done it before.
Under 5 for repeat visits.
Why Are We Doing This?
You have the manual air conditioning system and only reliably get air on high.
The German resistor pack Daimler specified most likely has committed or is committing suicide.
Step 1: Remove the Damper
The guts of the HVAC system are hidden behind the glovebox, so it needs to come out. Begin by opening the glovebox.
There are a couple things holding the glovebox in. The first thing to deal with is the damper. If you look on the outboard side of the glovebox, you'll see this:
It keeps your glovebox door from slamming open. It's held on with a simple pin-and-groove system:
Grab the beefiest part of the damper arm and pull it toward the rear of the Jeep so it unlocks. Gently pull the pin out of the big hole so the damper arm is free of the glovebox.
Step 2: Lower the Glovebox
With the damper removed, we can now work on taking out the glovebox without breaking anything.
You should see this:
The orange arrows point to the bump stops that keep the glovebox inside the instrument panel. You now need to pull the bumpstops down past the trim so they clear it.
The easiest way to do this is one at a time; I find the outboard (right) one is usually the trickiest. Don't be afraid to get a little rough with it. The left bumpstop actually has a huge fingerhold you can use.
Once you clear both bumpstops, swing the glovebox out. This picture might also give you a better idea of what the stops look like and how to grab them:
Step 3: Remove the Glovebox
Now we're clear of the interior and the glovebox can come out.
DO NOT USE TOOLS TO REMOVE THE GLOVEBOX.
There's at least one writeup floating around that wants you to use a flathead screwdriver to punch the glovebox off; it's totally unnecessary and you risk breaking the mounting hardware or marring the interior that way.
Open the glovebox about halfway between "normally open" and hanging down. (Roughly like in the photo above.) This will line up the openings in the glovebox mounts so you can pull basically directly backward.
Grab the glovebox as close to the mounts as you can on both sides, and give it a good yank one side at a time. Start with the inboard side—if you do the outside first, there's not always enough room to grab the inside.
Once both sides are free, you may have to wiggle things around a little to get everything to clear the opening. Take your time and set the glovebox aside once it's out.
Step 4: Remove the Blower Motor Resistor
With the glovebox out of the way, we've got clear access to our target:
Only 2 Torx screws and a connector stand between you and four speeds of heating and cooling.
Unscrew both screws and remove the resistor. Do not
unscrew anything else on the HVAC box; you just want to remove the 2 screws on the resistor itself. For clarity, they are called out with green arrows in the photo above.
With the resistor free, it's a lot easier to look at the connector and get it off. It's your typical "squeeze to unlatch" deal. (Hint: It's a lot bigger than you think it is.)
If you're extremely unlucky the connector may be damaged, but in my experience this is way, way less common with the WK than with the WJ. It also seems to be related to running faulty resistors for extended periods, so don't cheap out over an $8-9 part. If your connector is melted, seek professional help unless you're confident in your splicing skills.
Steps 4-99: Reassemble
Assembly is the reverse of removal.
As with taking it out, it's easier to put the glovebox back in inboard side first.
Putting it back on the hinges just takes a good shove; you'll feel it lock in, and it'll also be obvious you did it right when it's not flopping around.
Have a beer, you just saved $40+ in labor!