Sorry, but I think this is normal. My '93 300CE would run in this range until I installed a Jim Forgione temp resistor that turns on the fans earlier. I took a trip from Palm Springs to Parker AZ last year in July. Outside air was 115F. I cruised at 80 mph and the coolant temp held at 110-120F I was not concerned. I had an '87 300E and a '91 190E. They all ran on the upside of 1ooF in the summer.

I also have a E420. It takes a larger radiator. Since both are 124 models, this would be an easy substitution.
Anziani
'93 300CE 186K
'95 E420 120K