It sounds as if the sensor under the license plate is bad. I replaced mine with a 3.3k ohm thermistor and its been working great ever since.

I cut the stock wires as close to the metal thermistor as possible, drilled out the old epoxy and termistor bits from the metal sheath. Soildered the new thermistor to the two exposed wires, put the whole works into the stock metal sheath and filled it with epoxy. After it dried I screwed it back onto the mounting plate and its been working great since.

To test your display out, you can disconnect the sensor under the fuse box (on my 94 e320 at least) and put a 3300ohm resistor across the terminals (or any resistance in that range) 3300 should read about 72 degrees F.

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Daily Driver: 02 E430 4MATIC
In the family: '03 E500 // '04 ML500 // 64 220SE