The tube is there to draw air through the sensor when the blower fan runs. It serves the same purpose as the "aspirator fan" that showed up in the late model W126 and W124 cars. The fan has to be running to draw air across the sensor, hence why I suggested going straight for the silver box first rather than replacing the sensor (which is probably fine). If any of the buttons are pressed on the climate control unit, the fan should be running, at least on its lowest speed. The fan never cycles off completely.

Incidentally, the silver box is visible (barely) in your photo. Front and center below the pink vacuum pods is the cruise control amplifier. Behind it to the right on the firewall is a black plastic box, this is the relay box for the fan resistor control. Directly behind it is your silver box (you can just barely see the top sticking up over the black box) which is the brains of the whole HVAC operation. It's a pill to get to, patience is a virtue!

__________________
Current stable:
1995 E320 149K (Nancy)
1983 500SL 120K (SLoL)

Black Sheep:
1985 524TD 167K (TotalDumpster™)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)