unplugging connector puts system in to a it cant see the temps so it defaults to protect its self , runs fan flat out, also should put it in to a limp mode , on gen 2 cars it also opens the piloted thermostat and wont run to running temps over cools its self to try and protect its self, this all said and have no coolant in system nothing of the above will save it

 

If you have BMW ISTA you can activate the low speed and high speed fan using diagnostics. That would prove out the activation side of the electronics. You then need to look at the engine coolant temperature input side.

You can monitor the engine coolant temperature using the hidden menu (activated by the odometer reset button).

With the AC on (and the compressor running) I think the fan should run on low all the time.

Another thing I've seen (but not on Mini's) is air in the coolant system means the coolant temperature sensor is in air sometimes giving a bad reading. But in your case if the car thought the engine was hot surely the fan would have come on.

 

I would use a bi-directional scan tool to check that each component can be switched on (scan tool acts as the DME) - that may throw up issues - if so fix anything that is broken.

Look at live data for the temperatures when cold - are they plausible compared to where you live? if not a false signal back to the DME could cause problems.

Just checking back with you. The aftermarket parts, are they genuine BMW or known brands such as Pierburg or Febi (or other good brands) from a bricks and mortar store? Any no name internet specials are likely to be junk. Not saying they are, but just checking with you

Let us know what you find

 

I dorman sells a fan relay kit for 40 dollars U.S. I am sure there has got to be something there for that.
Aside of that. What I have always kept in mind is that the fan is a extension of the temperature of the car. Though it in and of itself is not smart quote un quote. It is controlled by the computer and the computer tells it when to turn on and off.
even though the electric fan you have may be new. It could be a result of the computer not getting the correct information of from the temperature sensor. And also to remember that vacuum filling the cooling with a air compressor and valve dredging coolant is the best method. Air in the coolant is not good. And can lead to burning up the heating element under the thermostat in the thermostat housing. Because the thermostat does not exactly open and shut according to the temperature of the coolant. It opens and shuts according to the temperature of what the computer wants it too, based on other variables. For me it's best to buy a genuine mini cooper thermostat housing with the thermostat sensor already included. As the thermostat itself is imbedded in the housing. So the item on top is in fact just a sensor. Saying I don't change thermostat sensors out on it. I buy the thermostat sensor and housing in a bundle and just use that.