Chosen Solution
iMac fan starts on full speed after shutdown Update (10/17/2015) Very interesting is, that when I’m using bootcamp and shutting down computer under the MS Windows, then everything is ok.
I would suspect bad capacitors on this machine. To get you to the correct guide to open it, please give us the last three figures of your serial number located on the bottom of your stand. UPDATE Now that I know your machine model, I do not suspect capacitors. Did you replace the hard drive? Try starting up in Safe Mode by holding down the Shift key on start up and let us know if the issue persists.
How about installing this app so we can see what your systems thermal management is up to here: TG Pro. Paste a full screenshot of the main screen so we can see all of the sensors in an answer.
