Date registered: May 2005
Vehicle: 1991 300SEL W140, Brabus, W220 facelift
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It might be the main fan drive (viscous coupling) or simply incorrect position of the fan shroud causing the fan not to obtain adequate speed.
I had that problem, and it gave exactly the symptoms as you describe.
In the beginning that was further assisted by one of the auxillary fans going wrong way. Anyway, the auxillary fans are controlled by the A/C thermostat - not the coolant thermostat - so you are on wrong track.
1991 300SEL W140, Brabus, W220 facelift
1987 190E 2,3
1987 Honda Accord 2,0