Kitchen Aid Superba side by side has intermittent problem with temperature control in both freezer and regrigerator sections. Freezer temp will increase to about +40F and refrigerator will increase to +50F. Temperature controls for both freezer and refrigerator are set to maximum (4). Coils are clean and there is no icing on coils or compressor. Compressor is not excessively hot to the touch. Both compressor and compressor fan will shut off. There is water puddling, but I believe that is from ice melting in the ice maker.
If I turn temperature control to off for a few minutes, then back on, compressor and compressor fan will begin to run again and both refrigerator and freezer will begin to cool again. This has been and on again / off again problem almost since the unit was new, but is now happening every few days.
Sounds like the thermostat (item 5 in Section 10) is sticking open.
When it happens again move the thermostat back and forth but not to off.
If the compressor fires up then I would replace the thermostat.
The reason not to go to off is that the problem may also be that the unit is sticking in in a defrost cycle and going to off may reset the adaptive defrost board.
Note: If the evaporator fan is running the you are not in defrost so the thermostat comes to the top of the list.
I replaced the freezer thermostat as suggested in the response to my post. That was several months ago and I have had no problems since. There is quite a bit of disassembly and routing of the sensor lead (for an amatuer like me, anyway) and you will need the doors open for quite some time, so you should think about completely emptying both the fridge and freezer to make access better. I just put everything in a couple of large ice chests for a couple hours and also found it a good time to give the interior a thorough cleaning. Good luck.