Why would your 2000 Jeep Grand Cherokee Ltd heater auto temp control suddenly blow cold air after 30-45 minutes of operating normally?

I have noticed that this problem only occurs with the headlights on. I am almost 100% sure that the problem is with the placement of the cabin temperature sensor placement (it is located between the two hot/cold blend knobs on the unit.

My theory is; when the lights are on, the incandescent bulb produces a high amount of heat that gets trapped inside of the control head. if you physically touch the temperature sensor, you will notice it gets very hot. Im sure that this would make the unit "think" it is hot inside the car and adjust the temperature to cool it off, while in actuallity, it is freezing inside the car.

I have tested it (somewhat). I held an ice cold beverage in my hand until my hand was ice cold, then i touched the sensor. It must've noticed the temperature change in the sensor itself, and suddenly, the heat kicked back on. Unfortunately, it didn't last very long.

Now, this is just my hyposthesis, however i think i will disassemble the control head and replace the incandescent bulb with LED's (which produce little to no heat at all). Hopefully this will solve the problem (I'll post back if it works!)