2012 27" iMac fan starts running at high speed when shut down and won't stop

My 2012 27" iMac is working quite well, even the fan doesn't behave strange as along as the computer is running or is in sleep mode. But it becomes strange when I shut down the Mac, because when the machine is OFF, the fan runs riot.

This is how I shut it down:

I select the apple-symbol in the menu bar and click on "Shut Down ...". After that I get a popup-window that tells me that without any further action the Mac would be shut down in 60 seconds (counting down). This window contains a checkbox where I can choose if I want to get all windows reopened after the next start (I don't want). I click on the right button that says "Shut Down". Then the screen turns black, and if I listen carefully I can hear some quiet noise form the harddisk, and after that I would expect that the machine would be completely off and emmits neither any light nor any noise.

This is true for light but not for noise. In exactly that moment when I would expect the end of all activities, the fan starts to run at highest possible speed. I didn't even know that it can run so fast and blow out so much air. But it does. And it wont stop. Even if I wait more than half an hour the fan keeps running at highest speed. And the Mac is NOT hot! When I touch it, it feels as cold as any other peace of metal that has room temperature.

The fan stops only in this two cases:

1) I physically disconnect the power cable. After doing so, I can wait as long as I want (I tried 8 hours during night). In the very moment when I reconnect the power supply, the fan instantly starts running at top speed and won't stop again (I lost patience after 20 minutes and then I pulled out the plug again).

2) I press the on/off-button on the back of the lower left corner of the Mac. In this case the fan stops on the spot and the startup-procedure beginns and everything is fine.

The fan also goes mad after long time in sleep-mode:

When I do normal work on my Mac (writing text, browsing in internet) I can hear the fan at a very low level. It is so quiet that I really must concentrate to hear it. When it is in sleep mode I don't even hear this low noise. I think the fan is stoped completely in this mode. But when the sleep-mode is lasting too long the fan jums into high-speed mode too. I noticed this today morning. Yesterday evening I set the iMac in sleep mode by pressing the on/off-button on the back of the lower left corner. Then I was watching TV for aprox. 2 hours and then i left the room and went to bed. Fan was quiet at this moment. When I came back in the morning I found the mac with the fan running on highest possible speed.

This happened before:

The day before yesterday I bought a new usb-hub. When the Mac was in sleep mode I connected the hub's UBS-cable to the mac and then connected the hub's power supply to the outlet next to the one where the mac gets its power from. Then I turned on the Mac and everything was fine. I worked some time on it (I guess 1 hour) then I pressed the on/off-button to send it to sleep, but this time it was different:

The screen turned black as expected, but the mouse-pointer was still visible for aprox. 5 or 10 seconds. I didn't try to move the mouse in this moment, so I don't know if it would have reacted on mousemovement. Then also the mouse-pointer disappeared and everything was as expected. Then I was away for some hours and when I came back I tried to turn on the iMac by pressing the on/off-Button. But nothing happened. I tried pressing the button for a long time (1 min) and tried to press it fast in rapid succession but nothing happened. My iMac stayed off. So I pulled out the power plug, did wait for aprox. 1 minute and reconnected it (at this time nothing happened, also the fan didn't start). When I tried to press the on/off-button this time it did work. My iMac did start and worked fine. But since this episode the fan gets crasy when the machine is shut down. It does so with the new usb-hub connected but also without. The hub is working fine. I also tried to disconnect the second monitor and all usb-peripherals (except the apple-keyboard with numeric keypad)

technical details:

iMac with 27" screen from late 2012

CPU: 2.9 GHz Intel Core i5

RAM: 16 GB 1600 MHz DDR3

GPU: NVIDIA GeForce GTX 660M 512 MB

OS: OS X 10.8.3 (12D78)

physical store: 120 GB APPLE SSD SM128E + 1000 GB APPLE HDD WDC WD10EALX-408EA0

Please can you help?

Thank you