Tnx for writing how you got around the problem with E3 Malcolm.
I am having the same problem and i followed what you did with the two pink wires and it worked.
I am at this moment in the process of ordering two thermostat but the part no you have gave does not Google well.
They should try this "Dishwasher Thermostat 90" this has given me a eBay seller for x2 at just over Tenner.
Kenwood suggest via the manual called "www.partmaster.co.uk".
The web link for the thermostat: http://www.partmaster.co.uk/cgi-bin/search.pl?brand=Kenwood&model=KDW243A%2FA&path=67231%2C111264%3A67242&shop=&query=Kenwood+KDW243A%2FA+thermostat&part=thermostat
Critch
September 2010