iMac Mid 2011 Display. Strange issue.

Hey!!

I have a 27" iMac Mid 2011 running Yosemite. EMC 2429.

One day, the monitor went to sleep and didn't wake up. (I hadn't updated or installed any new software for a long time)

Running the computer on an external display WORKS but the iMac monitor does NOT work.......

However.. Once the computer gets hot. The iMac screen starts working. From that point, it works as normal, for days in the heat or cold, unless it gets turned off, restarted or falls asleep, then the problem starts over.

If I want my iMac screen to work, I have to turn it on and using an external monitor, start up my 3D Rendering programs, start rendering very detailed models and also turn on a full screen HD video. I leave it like this for about half an hour and once the iMac gets almost too hot to touch, the iMac monitor turns on.

I have taken this into an Apple repair shop, they took it apart, charged me $60 to say it may be the graphics card. They also said that it is not the graphics card because it works fine on an external display and also once it gets hot. They had no answer real answer and gave it back to me unfixed.....