The aux fans are activated via the engine temp sensor and the A/C compressor switch. Your fans operating (or not) shouldn't affect your compressor operation (MB placed another circuit to shut down the compressor under certain circumstances for protection), but with the A/C on, the condenser radiator sits in front of the engine radiator and your engine is drawing heat from it, hence the higher temps.

Check fuses first (of course). Next, pull the plug off the temp sensor (near the front of the engine next to the valve cover just beside the water pump). The aux fans should roar on full if you do this. If this isn't happening, the aux fan circuit is at fault.

I can tell you much about diagnosing the circuit on the A/C side though...sorry.

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2009 ML350 (106K) - Family vehicle
2001 CLK430 Cabriolet (80K) - Wife's car
2005 BMW 645CI (138K) - My daily driver
2016 Mustang (32K) - Daughter's car