Make a complete check of your light to make sure thay are operational. (I like to do this when I pull up to a picture window.) Also check the license plate lights. If everything checks out okay you may have a corroded lamp socket somewhere.
Your outside temp sensor may simply have gone bad or something is amiss with the wiring. Try wiggling the parts while somebody watches the display. This may give a clue. The sensor is just behind the front bumper.
95 E320 Cabriolet, 131K