Intermittent problem with outside air temperature

Often the outside air temperature display on my 2001 Audi S4 will drop and then slowly return to normal temperature. It used to drop by 5 degrees C but in the last week it has gone
as low as -40.
The problem could be a simple problem with a sensor or it could e worn insulation somewhere inside an inaccessible wire bundle, or a dozen things I haven't thought of. I worry about asking the dealer to look at it because they could spend a thousand dollars of labor trying to track down a minor electrical fault.
Any advice?
--
John Carr ( snipped-for-privacy@mit.edu)

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John,
There is probably a sensor somewhere in the engine compartment that has a negative temperature coefficient thermistor in it. It's probably going temporarily open circuit - high resistance equals low temperature. Tho if you live in Yellowknife, that might be the actual temperature.
So, not sure of exact location but may be somewhere in front of radiator, on a flying lead?. That is where it is on my car, a 96 S6.
Tony 96 S6
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