BMW Repair: E46 air conditioner, connector wiring, temp sensor

Question
I have a 2000 323i and have been having problems with the air conditioner. It will suddenly the compressor will suddenly stop and hot air will start blowing. And then after a while, compressor starts up again. There is no pattern to this occurrence, and the duration of the problem varies also, from 30 secs to almost 10 mins.
I also noticed that I am missing a temp sensor from under the bumper, most likely ripped out from parking stone. Would this be the problem or something else?

Answer
Hammad, Replace the outside temp. sensor, connector, wiring, and or damaged plastic fender liner housing. Once the temp sensor is reading correctly the compressor will operate correctly. The A/C controls won't operate the compressor in too cold of weather as a safety feature.
-Evan