My 93 300E is having the same problem.
I dont think its the engine size...
My uncle also has a 90 300E. His is running hot also during the summer with the AC running.
I took it to the dealer and they said that the fan should turn on at 115. The dealer said it was some sort of sensor problem. I wanted a second opinion. Therefore, I took it to another repair facility. They said it was the Aux fan malfuction. They confirmed it by allowing the car to idle with ac on for a prolong period to raise the temp. They then measured the voltage to the fan. And sure enough, there was power but the fan did not turn. Go figure!