Great thanks Agile - I assume then that the thermistor has an operating range of 4k (hottest) - 12k (coldest) outside of which a thermistor error light will be triggered on the boiler.
Following the above logic, if the thermistor has failed and is showing a low value which is not out of range, then (depending on the user's setting on the HW temp dial) the boiler may think that HW temperature has already been achieved and not fire?
Chances are it's the DHW thermistor or pcb. Given it's intermittent just throw a thermistor at it for starters. You can't just stick the multimeter on the thermistor and expect to 100% correctly diagnose an iffy sensor...sometimes the lead wires are flakey or at certain temperatures it plays up.
The hottest temps will produce a resistance of around 2K at about 80 C but I wanted to ensure that with a 4 K resistor the boiler will still need to deliver some heat and so fire up.
12 K is about 20 C so would bring the boiler on with maximum power.
You finding the boiler fired up when fitting a 10 K resistor implies it was open circuit which should have been easily checkable by just measuring the thermistor resistance.
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