Was suffering this same issue on my '01 SL600. Finally got it fixed, but it wasn't cheap...

-New Fan Clutch ($411) with 2mm shaved off the actuator pin to lower the engagement temp to around 85c.
-New Radiator ($480ish)
-New Water Pump ($300ish)
-De-scaled cooling system w/vinegar, then flushed w/ a cooling system flush product.
-Custom-built T-stat, with 71c vernatherm swapped into an OEM housing in place of the stock 87c one ($150ish), from PTE over on MBWorld.
-Modified electric fan harness with resistor to engage at lower temp (free, thanks to good ole' kjcrf).
-Bunch of A/C work done also, ($1500). First, the car had a slow leak so the system was usually low on freon. Then in addition, the expansion valve was stuck, and the compressor was getting weak. All of this in turn caused the electric fans not to engage properly, or to engage too slowly when they did engage, because the internal refrigerant pressure sensor never sensed the correct internal pressure to engage the fans as required by conditions, which in turn further helped increase the coolant/engine temps.

Car now runs 81c on a normal day, 85c on a real hot day with the a/c on max. Everyone told me my old temp fluctuations were 'normal', but the M120 is an aluminum block and I just wasn't comfortable running around with 110c+ coolant temps, I felt eventually I'd wind up with warped heads if I didn't do something.

As a side note, when the car was new, it was always pegged at 85c no matter what. I assume the same for the W124. But as they age, all of these components (radiator, water pump, t-stat, etc.) slowly lose capacity due to internal and exterior aluminum corrosion, scaling, and general wear & tear. Truth is, 110c-120c temps really aren't normal in an 80's/90's Benz, at least in the sense of how they came from the factory. They are only normal in the sense of "well, a lot of them now have this problem...".

Your issues are some probable combination of electric fans being tired or not engaging properly, weak fan clutch, internal cooling system scale, or internal and/or external corrosion on the radiator, a sticky T-stat, leaky/weak water pump, incorrect coolant mixture for your geographical climate, or A/C system issues. The other thing that amazed me is, the mixture in my car was originally almost 60/40, coolant to water. Here in Florida you can easily get away with 30/70. Changing the mixture so that it was appropriate for the climate where the vehicle operates, plus adding some water wetter, brought the temps down a good 5c-10c just by itself.