I had a VERY similar problem on my 1991 300E. I had the manual to figure out the LOGIC of all the sensors in the cooling fan system. A post here suggested that I lightly tap on the suspect fan with a stick (handle of a hammer) because sometimes the fans get stuck and won't start up. I did this about 50,000 miles ago and it fixed the cooling problem and I've yet to changed a sensor or fan.
Just a suggestion before someone slaps down money and time.