I had a similar problem. My car has two fans, an electric aux fan and a mechanical fan.

My car also has a temperature switch for the aux fan, a switch for the mechanical fan and a temperature sender for the instrument panel.

It sounds like the switches are not hooked up properly or there is a short, a benz stock cooling is very strong and should handle up to 115F outside temp I think.

I would replace: the aux fan switch, the mechanical fan switch and the temperature sender and the thermostat. I will be one of those solves the problem.

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1996 E320
2000 C230 Kompressor
1988 190e 2.3 - 225K miles, owned for 7 years. I cannot say enough good things about this car. Very well built, even at 225 it ran like new.