On my C230, in summer traffic, AC cold, the electric engine fan runs almost all the time at slow speed. If the coolant reaches 106C, the fan kicks on high (and I mean VERY loud high -- jet enigne whine!). I tested the this by pulling fuses 19 and 30, disabling the coolant sending unit. The car kicks into "emergency" mode, and since it can't see the engine coolant temp, defaults to 106C and engages the fan at high speed.
It sounds like a fan problem, as it should be running at slow speed lots. The fan motor should be fine since it kicks on at 106C, but there is a controller issue somewhere. Also, even in 40C heat with the AC blowing ice cold (evap temp of 6C) my car has not one time kicked the fan to high speed. I've seen coolant temps of 101 or 102, but not 106 even once. If your car is doing that, it convinces me that you've got an engine cooling system problem, not an AC problem. The fan sounds suspect.
1998 C230 "Black Betty"