For my 2004 XC70...
I was also having a random problem with the outside temperature sensor reading on the dash digital readout. Some days, the reading on the dash seems correct. But on other days, when I start the car, the reading starts to drop until it goes to -40F or even drops out totally with "- -". I don't really care about knowing the outside temp, but the climate control system uses this temp to determine if hot defrost air is needed to defrost the windows. So when the dash shows a clearly wrong temperature (much too low), the auto climate controls try to heat the windshield by flowing with hot air, even though it is 90F outdoors and I only want A/C on.

Some owners say it only needs a new temp sensor inside the driver side mirror cover. I replaced the sensor, but I still experience the identical behavior.

So, what are my next possible solutions?
Is there a problem with the wiring connection between the sensor and the climate control system? I have volt meters, but I have no data on what readings I should expect.
Further, what can I do with the climate controls so that I can manually override the auto controls, so that the defrost air does not blow hot when I don't want defrost heat? How can I control the climate system using manual controls?
I know the dealer can probably fix this, but the cost of working with the dealer to repair this will likely cost more than the car is worth.

 

Which car, what year? Wiring diagrams can be found here for some models https://volvodiag.com/ewd-online-eng/

On some cars there are two sensors, one in each mirror. (only one is used for the CCM, and if it thinks it's too cold the compressor won't turn on either)

Did you measure the resistance of the old sensor and compare it to the new one? Could be an open circuit in the wiring where it flexes in the door hinge -