Thought i'd toss my 2 cents - i put up with the problem and kept getting worse, figured out running the machine hot mitigated the issue for a while, as long as the screen wasn't active, (when i went away, etc.) i could keep it running cool and as long as no one woke up the screen my remote applications could be accessed/files, etc.
Finally purchased a replacement and decided to go ahead (i've taken it apart many times for other upgrades) and tackled the baking of the graphics card just to see if it would work/replaced the, etc. thermal paste i had bought earlier to possibly do it and now.... the graphics card is fine... but my power supply was failing anyway. But that was interesting. Taking that thing apart isn't fun and only recommended for someone with steady hands and knows what they're doing. It took the entire afternoon. My wife said the iMac looked like it exploded from the inside out. I forgot to take a picture. So far 24 hours and graphics are fine, but i tore my hard drive's thermal sensor cable (i had replaced it with OWC's kit for an upgrade to 2TB so needed their external sensor kit)... and as always, ended up with an extra screw that i missed along the way putting back. LOL. So there will be a fan issue unless i use a software solution, but i'm going to recycle it anyway. Just was fun to try and do (since i am handy with taking computers apart).
Glad to be getting rid of the 2011, but it lasted me a long while - although could have lasted just a little longer - a testament to those Macs but i've had two defective macs (with defective video cards specifically) in a row and my wife's 27" had the 3TB drive recall and my older laptop had the screen/motherboard recall (i have to return it, they only did the screen and still has graphics issues. Graphics cards seem to be an achellies heel here on Apple's hardware?
Anyhow, was fun baking. Booted first try. Thermal paste is NOT FUN to deal with.
Already migrated to my new iMac 2017 - note: using thunderbolt adapter 2 to 3, setup internal network, you've got a super fast xfer method to transfer the system/accounts between old and new.
I know it's an old thread, but i saved it and finally got to do it! Cheers, John Q.
Apple ][ and forward, too many to list.