It's the "temp mix" control deal, and Yes, you've got an issue that I'm afraid is a dealer only fix. Even w/ a FSM, you're looking at hours of work, and the part is a dealer only buy. Have them do it, and don't go to a non-Mopar shop. They will NEVER get it right. went through it two years ago on my 97 XJ. Sux, I know. Feel lucky it is already on HOT, or you're double screwed in the winter. (Mine was stuck on cold when the cable broke.)
Here's the deal. It's an expensive pain, if I rememebr, and the dealer has had to re-do it twice since! (hang on to your paperwork, they will cover it after it doesn't work again.) Usually doesn't happen untilt the next season, when you're changing heat modes, but it will inevitably break again.
Take this hint, though. WHILE THEY HAVE THE DASH APPART, have them replace the defrost/floor solenoid. Mine started going a few months later, and it's a huge-ass pain as well, since the whole dash has to come apart again. This one only allows floor or face heat, and makes it impossible to use the floor/defrost, which is where I pretty much keep the control for five months a year (NW Wisconsin). When it goes it's either face or floor, nothign else.
This is a huge Mopar-PITA that should have been covered on every warranty because they all break, and are never right afterword.
Bitch nicely to the dealer, and make SURE you try it out a lot for the next few months after the fix. It will feel stiff for a bit, and then suddenly it will "pop" and be screwed again.
trust me, it sux big, and it's somewhere are $250 to fix alone.
Sorry to be the bearer of bad news.
good luck. Maybe live w/it during winter, and set aside a lil each month to fix it in the spring.