A couple of points.
1) Unless the latest firmware has been modified there is no way that the board temperature sensor can switch off the unit - it only supplies information to the fan controller.
2) the drives themselves have temperature sensors and that temperature is available in the SMART data. Drives generally start having problems if their temperature rises above 50o C for long periods of time.
What most people here are describing, if the power supply provides 12v@3A under load, is a component on the board (possibly the SoC) that has been over stressed by a voltage spike and is now very sensitive to external temperature. The units with out drives will quite happily run in a 70o C environment, with drives that has to be a temperature that keeps the drives below the 50o C danger temperature.
When measuring the voltage from the power supply it is essential that it is done so UNDER LOAD. A faulty power supply can quire easily supply 12v at no load but end yo supplying only 5v or 6v under load and these units require a minimum of 11.5v to work correctly.
Another thing, it is almost impossible to diagnose component failure by way of a forum post. I could tell you to get a can of freeze spray then strip the unit of its case, power it up and then start spraying individual components to find out is one is temperature sensitive. The problem is that even if you did find a dud component could you replace it even if you could get the correct replacement?