Go to Radio Shack and pick up a couple of resistors (yes you still can find those there buried in the corner in the back behind the r/c cars)
Get a 10 k, a 3.3 k, and a 1k

Open up the fuse box and carefully undo the 6 screws and lift the fuse assembly up, be careful not to short anything out. In the spaghetti pot of wires there is a 2 pin connector with a brown and green wire. This joins the sensor at the bumper to the instrument harness. Unplug the harness connector and apply each resistor to the instrument side of the harness. 10 k should be about 50 c or 120 F. 3.3 is about 20 c or 68 F. 1k is about 0 c or 32 F.

Measure the other side of the connector going towards the probe. Based on temperature the resistance ought to be about 5 k for this time of year.

FSM 54-6320 has all the details and the temperature/resistance chart.

Based on this you should be able to tell if the display or the probe is bad.

__________________
The OM 642/722.9 powered family
Still going strong
2014 ML350 Bluetec (wife's DD)
2013 E350 Bluetec (my DD)

both my kids cars went to junkyard in 2023
2008 ML320 CDI (Older son’s DD) fatal transmission failure, water soaked/fried rear SAM, numerous other issues, just too far gone to save (165k miles)
2008 E320 Bluetec (Younger son's DD) injector failed open and diluted oil with diesel, spun main bearings (240k miles)

1998 E300DT sold to TimFreeh
1987 300TD sold to vstech