There should be 4 wires coming out of the insulated white cable:
Brown - active in
Black - switched active return
Blue - neutral
Yellow/Green - earth
The brown is active in and connects to one side of your thermostat. It also loops off the thermostat terminal and goes to the white connector. This is the supply to your door switch. The active return from the door switch is the red wire which goes to the active terminal of your light.
The black wire is connected to the output terminal of your thermostat and returns to the compressor to switch it on and off.
The blue neutral wire will connect the the neutral terminal of your light. The yellow/green earth wire should be connected to metal, usually via one of the screws.
If this matches the layout of the wiring of your fridge (it should), then with the fridge unplugged, you can join the two wires connected to the thermostat together which will bypass the thermostat. Without another form of thermostat, this would cause the fridge to run continuously. With the STC1000 connected, it will now control the fridge without the standard thermostat causing any problems.
If the wiring is NOT how I have described it, then don't touch it. Maybe post some clearer photo's showing all the terminal connections.