Same as you my fan was locked.
I just took it off, the temperature is a sturdy 90 degres, never more. The Electric fan at the front kicks in when the temperature is too high.
You don't need a specific tool to hold the pulley, there is a little hole at the back where you can insert an allen key that will rest on the pump and this will able you to unscrew the fan.
I did it few times with the rad on but some nicely suggested to remove the top of the rad to be able to tilt it slightly, this will save some knuckles

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E300TD year 2000. RUSTY SOLD
cost a fortune to maintain on the road
but run well on WVO
Second Merc died due to corrosion ( NOT rust) How can mercedes get away with that for so long?
Third lasted a month then went away...
Fourth now... Corroded too...