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A new member, pleas take the time to review, for your benefit:
FYI, the forum index is grouped according to chassis / platform designation, usually one letter followed by 3 digits / numbers, and sections cover all engine versions the chassis came with.

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Moving this to the W206.

 

If the fans are running at a low speed and turn off themselves after a couple of minutes, that is normal behavior. This happens usually when:

A DPF regeneration was in progress and got interrupted.

The regen has finished very recently and the fans are running just to lower the engine bay temperature to prevent excessive heat soak.

 

Welcome to BW.
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If I'm not mistaken, the C43 is gas powered so there is no regen. To answer your question, yes, the fan does continue to run after engine shutdown. This is meant to cool the radiator down to a nominal temp. They will also start up without the key in the ignition after the engine has ran. I just replaced the fan in my CLK last year and mine does it all the time. I thought it was abnormal until talking to an indie in the area. Now it will run for maybe a minute or so after and then shut down. I am waiting on my new 22 GLC 300. It did the same thing on the test drive.