Fixed this problem over the weekend, wanted to pass along the successful solution for future reference:

Bought a 99 WJ about a month ago. When I was looking at it, I noticed the heater wasn't working. This is obviously a big issue going into winter in Utah, and the dealer said he would fix it. He told me later it cost him $600 to do so.

Last week, I was running the heater and the blower stopped. I messed with some stuff on the controller on the dash, and it started working again. "Strange. " I thought. On Friday, it stopped again and messing with the dash wouldn't get it working again, so I started googling.

I found on WJJeeps that the "blower motor resistor", particularly the plug that goes into it, is a known issue.

http://www.wjjeeps.com/blower_motor.htm

I dug into it and found, sure enough, my plug was burned and half melted away, and so was some of the insulation going up the wire.

Looking at the resistor, it had a manufacture date of '09, so it obviously had been replaced at some point. I wondered if that was what they supposedly charged the dealer $600 for - to replace the resistor. The plug, however, was obviously original and was (at least now) the problem.

I opted for the soldering solution. I chopped the plug off (careful, one of the wires is "hot"), used some spare heavy-gauge wire I had to solder 3 lengths of wire onto the pins on the resistor the plug goes onto, used heat-shrink to isolate them from each other, put the resistor box back together, then spliced the "extra" wire I had soldered onto the resistor into the leads that were going into the burned plug. I spliced using the crimp type connectors, then wrapped them all in electrical tape just in case.

Works perfectly now!

 

I effected an almost identical fix on my 2000 WJ a few years back. Rather than use heat-shrink, I used tight fitting insulation over each wire, once soldered directly to the pcb.

Apparently there is an official jumper fix available – but quite how you are supposed to fit it once the plastic connectors have melted into one, would seem a problem.