Screen intermittently going black even after backlight board replaced

My 2012 iMac 27 inch started acting up a month ago. Screen goes black for about a second, then returns to normal. Sometimes this happens once, other times it repeats itself several times before returning to normal. Computer is on the whole time and I can continue working once the screen returns to normal.

An authorized Apple Service center looked at it. Hardware tests were normal. Ended up replacing the backlight board. That did not resolve the issue.

I've done several "tests" and found the following:

1. When a second monitor is hooked up, the screen does not go black when the main display does.

2. When the screen goes black and I have a flashlight shining on part of the screen, I can see the windows/text/images that are supposed to be there.

3. Reseting the SMC and PRAM had no effect.

4. When I increase the fan speeds (using iStat Menu), the problem disappears. When I set the fans to their defaults, the GPU Die and GPU Heatsink temperatures increase by 40 degrees. The screen will intermittently go black again within minutes of the temperature increase. Other temperatures increase as well, but I have focused on the graphics-related temps because of the problem.

The Apple provider seems fixated on the problem being the display. Since this appears to be a temperature sensitive issue, I am trying to rule out other possible causes before shelling out about $800 for parts/labor.