I have just done this after failing to find any guidance on DIY forums such as this. However, it turned out to be so easy i thought i'd share.
The 'stat is mounted behind the fridge setting dial at top dead centre of the compartment (by the light).
Make sure the fridge is unplugged! Remove the four (?) securing screws and the panel, together with lamp and door switch should drop down. Make a note of where the three wires connect to the 'stat - there should be an incoming live (brown), an outgoing switched feed to compressor (black i think) and a third wire which goes to the bulb (via door switch).
Remove the spade connectors (pull off) and winkle the white settings knob off with a small blade. The 'stat is retained with a wide nut which can be removed with a pair of long nosed pliers. Pull the thermocouple probe out of the housing tube; there may be some rubberised filler with an obscure function.
The new probe should be carefully unrolled and gently pushed into the tube which guides it to the back of the fridge compartment. Push it all the way in until the 'stat is approximately aligned with the fixing hole in the plate and replace the fixing nut with the pliers.
Reconnect the spade terminals (my 'stat was not identical and i had to check which terminals were which with a multimeter and a can of freezer).
Refit the plate (there's an in-line connector which needs seating out of the way) and replace screws - restock the fridge, plug it in and enjoy!
Bullimore
September 2010