Hi John, This will probably be another of my useless posts but I'll see what i can do.
in the summer the fan will be very loud when hot outside and the air is on, schoolbus sounding. When your engine is cold and you first start it the fan should spin fast and hard and make that sound for a few seconds until the fluid in it softens up. Other than that I have read and dont recommend sticking your hand in there.
The auxillary heater pump allows the coolant to circulate at an idle, when the flow is slow.
Your temperature seems fine. but you might have either air in the heatercore or the pump isnt working. You should however get heat when the engine is reving above an idle.
95 E34 530I V2.37
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John F. Kennedy