Chosen Solution

The system was not giving fan spin-up before display replacement. I tried two separate replacement displays. Both displays are the same and are listed as being compatible with the Late 2012 27-inch iMac. The identification on the displays lists them as LM270WQ1 (SD)(F1) The displays appear to be in good condition. When I install them, I get full-speed constant fan spinning. What should I do?

I am a doofus! The solution was simple. I had mistaken the LCD backlight inverter flex ribbon cable for the temperature sensor and had failed to notice that both of the replacement displays I had tried did not actually have a temperature sensor installed. I installed the actual temperature sensor on one of these displays and of course the issue was resolved. Looks like the problem was just due to me confusing the function of internal parts!