My e39 reads -40 degrees for exterior temp at all times, and although I replaced the sensor, under the passenger front wheel-well, it persists in this unacceptable behavior. Is there a reset button for this feature. I have consulted my Bentley's book but it doesn't go into this type of detail needed.
Any input?

I can get the weather report on my phone. However I have heard that the exterior temp reading somehow has a bearing on the AC/Heat system causing the interior temp not to act properly.
Is this a valid concern? Anyone out there have some more info on this matter?

The temp sensor is located in the middle of the grille and with a winter front on no ambient air gets to the sensor so heat from the radiator gives you a false reading. The sensor should be relocated on the rad support close to the drivers side headlight

Wrong. The temp sensor mounts in the lower inner wheel well extension. The sensor is either faulty, or the wiring harness/sensor has impact damage. The dealer has a replacement harness if needed