The funny part of this story is that we are officially becoming wusses. It used to be we'd drive through rain in 40-degree weather sans top, doors, or any semblance of reason with nary a worry. Nowadays, the heat stops blowing through the dash vents on our '01 TJ, and after the first cold spell, we're under the dash figuring out how to fix it.
Apparently, this problem is an epidemic in '97-'03 TJs. From our research, the '98-'01 TJs and XJs have the same specific issue we had: the panel/demist door actuator pushes too hard on its little plastic arm, and over time, breaks the thing clear off. The dealer patiently explained to us how it would cost $1,400 to fix.
They based this estimate on a complete HVAC box removal, with accompanying A/C evacuation and recharge, not to mention parts and labor. We got in there, and with $1.98 worth of super glue and a random screw, nut, and washer from our parts bin, we were back in comfy, cozy, wussy comfort. Sure, we felt like sellouts for the return of the nice HVAC function, but hey, we were comfortable sellouts. If you find yourself in this situation, here's how to save $1,398.