1994 E-500..the temp gauge of external ambient temperature started giving readings approx. 20 degrees below the actual temperature outside ( ex. if it was 39 degrees outside it would read 19 to 22 degrees on the gauge). Curiously, if I,ve gotten in the car after it has sat overnight the temp gauge reads normally, however within 2 minutes it starts giving the wrong reading. I,ve replaced the temp sensor wire to no avail. I can't believe it is the display module as it gives an accurate reading for brief periods of time. Suggestions?

You mention replacing the wire. Did you replace the sensor as well? If you did, then you may have a bad connection somewhere. I'm betting on the sensor. New does not always mean fixed..

Ambient temp sensor
 

I replaced the wire and the sensor. The temp gauge acted the same with the previous wire & sensor ie. normal reading initially then -approx 20 degrees off within 2 minutes.

Well, if you insist, This now sounds like you may have a thermally related fault in the sensor module. if the fault is repeatable each time you start up,and it has occured wqith two different sensor assemblies, then my best guess is some kind of thermally related problem in the sensor module..

Before you replace any more parts I suggest that you test the display module and sensor/cable separately.

To test the display module, connect a resistor (any value from 1,000 to 20,000 ohms will do) across the sensor terminals, along with a 12 volt power source across the power terminals (on the rear of the module). If the temperature reading fluctuates or varies considerably over time, you can be confident that the display module is faulty (very rare).

Conversely, if the temperature display remains steady, then connect a meter across the sensor contacts of the connector plug. The resistance reading should be steady (+/- 100 ohms) if the ambient temperature is constant. Also, have your assistant jiggle the wiring harness (while you watch the meter) to determine if you have a loose contact or ground in the sensor cable.

Too bad these tests weren't done before the sensor was unnecesarily replaced the first time. Another thing to check is whether they actually replaced the whole cable or just spliced into the old one. If it was only spliced, the problem may be a bad connection in the original cable that's still there. If they did splice (a no-no) have them redo the job properly.

Hope this helps. Let me know what you find.
Barrie