Your sensor went bad or is disconnected (or absent). -35 degrees is the default reading when the computer receives no input.
I have seen the piece you are talking about (behind the fog light). I now believe that it may be the temperature sensor. I say this because there is one exactly like it inside the door -- I suspect it is used to activate the cold weather accesories).
You can get the temperature sensor from the dealership (pricey), bavauto.com (more reasonable; if you cannot find listed on their website, give them a call -- they can get it for you), or just try google and pick a place that looks reputable. Browse the forum. I know we have several threads listing good parts websites.
Good luck, and welcome to the forums.