The ETM for my 1983 300SD says the aux fan switch closes at 100C (212F). Probably similar on your 300D as we use much the same engine.

If you unplug it and short the two feed wires, the fan should come on. The switch is the red thing with two wires on the receiver-drier - near the driver's side headlamp(s). (Don't confuse it with the (larger) pressure switch, also with two wires). That will verify whether the fan works. It unscrews. On the early r-d (like my 380SLC) you don't lose freon; on the later ones, you do, contrary to what has sometimes been written on this forum. Pix on my site in the a/c piece.

Test it in boiling water with an ohmmeter to see if the switch works - I would guess you could raise the boil temp a few degrees by adding common salt. Resistance should fall from open circuit to next to nothing at 100C.