Here's a quick how-to on taking out the display unit:
This was performed on my 1993 190E's unit. I have an 1986 model year unit and its significantly larger and less integrated. I just assumed the 89+ models were when there was a change over. I saw pictures of units from 89 w126s and they looked like this one.
Evidently late w126, w124, w201 units all the boards and displays can be interchanged as indicated in this thread:
http://www.peachparts.com/shopforum/diesel-discussion/289232-exploring-vdo-outside-temperature-display-w124.html
If you car's display works but the temperature is inaccurate, you should replace the temp sensor at the front of the car, I think, in the case where the numbers fluctuate all over the sensor should be replaced as well:
http://www.peachparts.com/shopforum/tech-help/264842-outdoor-temperature-sensor-replacment.html
1) Remove Cluster from Vehicle
2) Remove These Screws, to remove the unit.
3) Remove The plastic connector surrounding this pin so you can fit it through the opening
4) Remove the display from the cluster
5) Remove these two screws, and then remove the cover
6) Removing these two screws will disconnect the LCD display from the driver board
7) Replace Capacitor. Remember the black heavy line indicates the location of the negative connection. Maintain this orientation when soldering in the new capacitor. When replacing capacitors, rule of thumb is maintain same storage rating, use same or high voltage rating.