There are a couple of excellent threads on this topic. There is a fairly simple test noted in one of the following discussions for determining if the problem is due to the display or the temperature probe or thermistor, which is located under the front license of the (at least) the early 90s versions of the W124 cars.
I replaced the thermistor on my í92 and it works fine. Should there be an interest, I have 3 of the thermistors. I bought a few at Allied Electronic. Iíll sell them for $7.00
Here are the articles:
outside temp LCD
87 300e outside temp gage