Would be good to add year and model to your signature. Depending on the year and model----

The secondary air pump should run when the engine is started and shut off when the engine goes from open to closed loop, when the cats are hot enough to control emissions. However, it does not impact coolant temperature.

The electric fan should run run a test when engine is cold started. It doesn't go to full RPMS and it doesn't last long. On some models the electric fan turns on when the air conditioning is engaged. I don't remember if engine has to be at operating temp before that happens.

Do you know if the thermostat is working properly? Could it be stuck open?

Is it possible the temp readings you are getting are celsius?

Even though the clutch fan is new have you tried to see how easily it turns when engine is cold?

I would also test the new temp sensor.

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X5 4.6 2002 Black Sap, Black interior. 2013 X5M Melbourne Red, Bamboo interior
Dallas