There is no direct test other than performance. One might state that if the control signal goes in but the "comp on" signal doesn't come out then it is disfunctional. The problem with that assessment is that its job is to cut the compressor for precise reasons. These reasons are only semi-spelled out. Temperature is the obvious (from the wiring diagram) criteria. I am pretty sure that engine speed both slow and high are monitored and battery voltage (or charging rate).
The temp switch involved is S25/5.
Bosch Master, ASE Master, L1
33 years MB technician