Maybe a sensor or resistor of some sort. When certain sensors have a certain temperature they may activate to provide a certain current and if there is a break down somewhere you are not getting that current or not reaching the temp because of a fault. Track down the part that is causing the fan to engage when it is cold and remove it. Maybe a relay or something. Then turn the car on and see if the fan is engaged. Let it get to operating temperature and see if it has a default setting to engage it. If not, replace that part and redo the test. Then check the sensors and resistors. Relays are the easiest so I say start there.

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1990 190E 3.0L