The outside temperature display on my '86 300 had problems with the display gradually getting black. The black started in the upper right corner and slowly spread across the right third of the display. When I finally replaced the display, it was only reading one digit. I purchased a used display on Ebay for about $40. The 'new' display had the 5-pin connector instead of the original 4-pin. There is a MB TSB out on how to wire in the new connector. It turned out to be pretty easy. Now I have a good display.
The accuracy problem is likely separate although, if the display can only give certain digits, that may give false reading. There is no trimmer adjustment in this system. The temperature sensor under the front bumper connects directly into the display module in the dash.
If my memory is right. The sensor is a temperature sensitive resistor or thermistor which has the resistance go up as temperature goes up. If you are getting high readings, the sensor may be bad or maybe there is a poor, high resistance connection in the wiring from the sensor to the module.
The cable from the sensor follows a winding path from the fender up to under the fuse box where there is a connector to wires which then go to the dash and the module. To reach that connector, you need to remove the fuse box. Talk about a dumb design! The PO of my car had a new sensor installed and they just cut the old cable up near the left front headlight and spliced in the cable from the new sensor. They taped it pretty good and it has worked for years.
If the sensor itself is going bad, there is a low cost replacement thermistor which you can buy at Radio Shack or probably any good electronics parts place. I don't recall the part number but you might find it in this forum with a search.
