I've not done this on my W124, but I don't belive the temperature sensor is directly behind that vent. There's a small fan that blows the cabin air down a long tube towards the sensor.

You should be able to vacuum the dust up and place a 1cm x 1cm piece of paper over the vent to see if the fan is working. The fan should be strong enough to hold the paper in place over the vent in the ceiling.

I'm not entirely sure how to check the temperature sensor itself, I think it's location changed over the production run. It may be buried in the dash somewhere.