This is my experience - I am not sure about a W123 but I had similar problem with my 190D. The temperature gauge did NOT move. I grounded the cable at the sensor to ground and the gauge read 'RED', i.e. max value. This indicates to me the cable from sensor to gauge is OK and the gauge is not stuck. I replace the sensor and everything works now. I don't think the sensor is repairable and it not that expensive. It is just a resister registering different values at various temperature.

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Not MBZ nor A/C trained professional but a die-hard DIY and green engineer. Use the info at your own peril. Picked up 2 Infractions because of disagreements. NOW reversed.

W124 Keyless remote, PM for details. http://www.peachparts.com/shopforum/mercedes-used-parts-sale-wanted/334620-fs-w124-chasis-keyless-remote-%2450-shipped.html

1 X 2006 CDI
1 x 87 300SDL
1 x 87 300D
1 x 87 300TDT wagon
1 x 83 300D
1 x 84 190D ( 5 sp ) - All R134 converted + keyless entry.