You are correct, you only need paste between the CPU / GPU and the copper plate. If it is a cooling issue, the entire system should shut down, including the screen and the fan. Can you send full pics of your wiring (power, VGA, U10, all that good stuff)?
Attaching the thermistor is one of the last steps in the manual. If it's not connected, the PMS should never be able to shut itself off like that.