I made life easier for me by not using sockets at all... just all wires (from the STC-1000, and the heater) going into the existing connection points on the compressor in the fridge. Yes I had to add a chocolate block ("screw terminal", I think is the proper name) for one extra connection.
The exact wiring will depend on your fridge but basically you replace the live feed that comes from the fridge thermostat and goes to the compressor, with the live feed from the STC-1000 "cool" terminal. Then just provide the supply to the STC-1000 by connecting up the live and neutral (and earth) from the existing fridge connection points where the mains cable comes in.
That's the cooling side done.
You're left with the heater. Neutral goes to the existing neutral connection point where all the other neutrals go (you can usually make room by removing any connection that goes to light or thermostat), earth similarly, now and you just need to add the aforementioned screw terminal to connect the live heater wire to the live wire from the STC-1000 "heat" terminal.