Hi Bazz,
You need to replace the S plug and socket, once they heat up they're best replaced.
But why? The 12N and S connector are a simple push fit, and need careful use and maintenance to achieve long lasting, good electrical connections. The deficiencies in the design include:
1. The brass pins have a slot cut in them so they can be prised apart and restore a tight electrical connection - loose fitting means high resistance and the connection heats up.
2. They are made of brass, which will corrode in UK weather - and that means high resistance and the connection heats up.
3. The pin allocation was changed about 10 years ago - and in what has turned out to be a mistake, the fridge return was changed to the centre pin - which is also the guide pin to align the plug and socket - easy knocked, this afters the connection, and the connection heats up.
The fridge draws 10+ amps and this all needs to return via that central pin, and pin burn out is a common problem.
The only permanent solution is to change the twin 12N+S for the superior 13 pin ISO connector...
Robert