Testing AC components
This might help. Paragraph four goes through how to check the electrical connection to the AC compressor. P.S. Don't forget to check the fuse !!!
I had a problem with my AC and I found an answer on a different site. I'll post the info here in case anyone else needs it.
The AUX Fans are the two fans mounted in front of the radiator. They are triggered on when your engine temp exceeds 115C, OR the AC is turned on, AND has built up pressure. If you are low on freon, the system will not build enough pressure to turn on the AUX fans. This can be a big problem, as I will explain later.
To test the AUX fans, turn the key to the "ON" position (engine does not need to be running), and short the two contacts on the top of the AC drier. The AC drier is located behind the driver side headlight on the 560SEL, and possibly others. When you short the two wires together, you should hear the fans turn on.
To test the AC compressor clutch, turn the engine on, and turn off the AC. The forward portion of the AC compressor should NOT be spinning. If you short the two contacts on the SIDE of the AC drier, the AC clutch should engage and the forward portion should be spinning.
As I mentioned above, running the AC while low on freon causes high engine temperatures due to a slight domino effect.
First, it's hot outside, or else you wouldn't be using the AC.
Next, running the compressor without enough freon is harder to do, causing more work for the engine (I know because last night, while adding freon, the engine smoothed right out)
Next, because you are low on freon, the system will not build significant charge to trigger the AUX fans.
So now you have an engine, that is doing more work, on a hot day, and does not have aux fans running..... that will lead to a HOT engine (>110C).