I may have the same problem - the water heats up ok when the central heating is on, but when it's off the boiler fires up for a few seconds then switches off, so the water never heats up. If it was a thermostat problem I would have thought it would happen when the central heating was on.
If it is a combination boiler, it would probably be a diverter valve diaphragm problem. They are made of rubber and split, when they split they can only operate for a couple of seconds.
The boiler man, April 2009
Sounds like the diverter valve or motor part of it.
