Update (Feb 2018)
Thanks to a good friend I was able to disassemble the iMac and extract the graphics card. We put it in the oven and baked it for 20 minutes at 200 degrees Celsius. We cleaned the iMac, replaced the thermal paste and reassembled the iMac again.
And what do you know, it worked again! It works for the last couple of months and I guess as long as I dont use it daily again it will work fine. I make sure that it does not get over 45 C for longer periods of time and hope that in doing that, I can extend it’s life even further.
After six and a half years of heavy use, my main computer, a mid-2011 27″ iMac, is on the Fritz.
It is currently unclear if it is the graphics card itself, some related hardware, or just a worn cable. Maybe I am gonna be surprised and it is something completely different. What annoys me most is that it could be related to an call-back from 2014. I did not notice the re-call at the time and it apparently expired in 2014 (that is the reason why it is only available in the WayBack Machine).
I already emailed a local authorised service provider. Once I hear back from them, I will bring it in to get an analysis and a quote. Based on that, I will see what my options are.