2003 mitsubishi outlander temperature control knob would get stuck while turning..and finally snapped off and broke

Probably less than 30 bucks and it just slips on

Test for stuck relay. With everything off but key on, feel the tops of relays for a warm of hot one.

With hot battery, turn all off, wait 10 minutes and then feel of all relays to see if one is warm or hot. Stuck relay can cause this.

Follow the cable.. It's the white piece that the cable connects to. Some kind of spring doesnt push the white piece forward far enough to select a hot temperature. You can adjust it yourself from the driver's seat at a red light. It feels like flat lever against the dash/transmission tunnel. Push forward for heat, pull back for AC. There's a spring busted or something and the knob can't overcome the required force... Just manipulate it manually. You can see the white lever mechanism clear as day if you open the driver's door, crouch down and look for the big white piece. My guess is that it has a internal tensioner or spring that crapped out.

Replace heater/ac control assembly

http://outlander.net.ru/Vitaly/CHASSIS/03/all_of_car.pdf

I have the same problem. Finally found this repair manual on line.
Pages 52A-27 & 28 give a break down of the seat.
The reclining knob is broken #23. It engages the reclining cable #31.
Look closely at the underside of the knob to see if part of it is broken off and this will indicate we share the same problem.
I've always let go off the knob when reclining the seat, but in the future, I'll be slowly releasing it.

replace the knob

check the fuse for the dash lights

The knob is probably broken. It should work after you replace it a good one.

there is a recall for corroded connections on wiring on climate controls the service man at mitsubishi dealership said i am taking next day off to be repaired