27" iMac, Erratic display, Possibly overheating?

I have a 27" iMac model EMC2429 which seems very hot after about an hour's use and sometimes the display goes quite erratic. I have ran the Apple hardware diagnostics and this does not find any problems.

If the system is overheating could this cause an erratic display or is it more likely that there is a fault with the graphics card?

If the problem may be with overheating what cause of action should I take?

The fans seem to be working and I have blown away any dust debris from inside the Mac.

I have done some further testing on this iMac and it appears that the main screen is overheating.

When the screen is connected, the iMac becomes very hot after about 10-15 mins and the whole system locks up.

I have removed the screen and tried running the system with an external monitor attached.

With the main screen disconnected the system is no longer getting hot and seems to run reliably (although with the LCD thermal sensor disconnected, the fans operate at full speed all of the time).

Is it possible, the problem may just be with the thermal sensor for the LCD screen?

When the screen is connected, the fans hardly operate even though the system becomes very hot.

I thought that the Apple hardware diagnostics tested all the thermal sensors but no errors were detected?

Is the LCD thermal sensor available separately at a reasonable cost?

I obviously don't want to pay out too much on such an old machine.