I will check the high speed relay.  
A stuck relay would make the fan come on when started.  However, I would think that it wouldn’t take 5 seconds after starting to come on.  It seems like something (ECU or AC) is turning it on 5 sec after it starts.  I am out of ideas and this is a good suggestion.  Thanks

Perhaps the high speed relay is stuck.  The high speed relay is mounted on the fan housing in the relay pack.  The relay pack contains the high speed relay and a voltage reducing resistor.  You might try testing this relay to check functionality.

Ken

I have a 2003 Mini Cooper R50.  I just replaced the transmission and I noticed the radiator fan comes on high about 5 seconds after the car is started...cold or hot.  Fan goes off when I turn key off.
The AC and Defroster are off.
I can read the temperature sensor from my scan tool and it is reading correctly.  Temp goes up as engine warms.
coolant level is ok
I reset the ECU (Test 19 -21 Reset) and it still comes on.

Is there some other temp sensor that I’m missing?

Thanks