Help needed with 99 e46 cooling fan runs continuously after key removed

After a long trip, 4 hours all highway but got stuck in construction detours several times, I get out of the car (e46) and the radiator fan ran on continuously.
Pulled each fuse in fuse panel individually but made no difference.
Pulled each of 3 relays in black box under hood in front of driver, no difference. Also noticed 5 or six fuses in covered black box 1 inch square but did not remove them to test circuit for open.
Disconnected battery, fan stopped.
Drove the car back home with power plug to fan disconnected. Temp gauge showed no tendency to overheat.
What am I overlooking and where is it?
Overheat switch that sends power to fan?
Fan relay? Where is it?
Thanks in advance to all who send help. I have to drive to work tomorrow. (highway)
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why do you think this isn't entirely normal behavior?
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daytripper wrote:

the fan would continue to run, The battery would eventually exhaust itself if I did not disconnect the power to the fan. It is NOT normal behaviour because after 48 hours of not using the vehicle, I plugged the connector back in and the fan continued to run with no key in the ignition.
Disregard my request for help. I started disconnecting all sensors on the engine with the fan running, 5 hours after I shut the engine down (engine cold) I found that the connector at the front of the engine lined up parallel to the axle just under the valve cover did the trick. I reinserted it and the fan shut off. I wish I knew which sensor this was. It is also located on the exhaust side of the engine.
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Logic says it measures water temperature. From behaviour I'd say the sensor's resistance increases with temperature, so with the connector off (infinite resistance) it assumes that nuclear fusion is taking place in your engine and it attempts to cool it down.
You can check out parts for your car by going to http://www.realoem.com/bmw/select.do and entering your car's data.
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Jan Kalin wrote:

this link there is an ad to sell trouble shooting manual but after paying the $18.99 was unable to download the manual and the contact us link where I sent two questions was also ignored, I cancelled my order because I need my car and can't wait around while the internet gods work to complete transactions.
Still driving around with no fan .................................. overheat?
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FFF wrote:

I thought the radiator fan was mounted on a viscous clutch: cold engine, grip (no turn), warm engine, slip (and turn).
Wouldn't this be your auxiliary fan?
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E46 with M54 engines don't have fans mounted on the water pump; they have two electric fans.
Floyd '01 330xi
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That fan is thermostatically controlled. Let it run until it shuts itself off. It can run for as long as it takes. If it is still running after an hour, then I'd be concerned, but then I'd watch it to see if it repeats.

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J Strickland wrote:

connector I let the engine cool off with the hood open. 4 hours later , when I reconnected the power to the cooling fan, it ran again with no key in the ignition and engine not running.
There must be a relay that the control circuit closes, this relay may be welded closed or the control circuit is telling the cooling fan to run. Any one know where the thermostat or temp switch for the control circuit is? Anyone know where the relay for the cooling fan is? There could also be a fault in the wiring harness that tells the control circuit that the cooling fan should run.
In any case, the car runs at normal temperature with no cooling fan connected electrically. Of course I did not idle or remain stationary for any length of time. I suspect this is when the cooling fan would run. The cooling fan has never operated with the engine off for as long as I have owned the car, for several years.
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