Aparrently the thermometer isn't broken.
I looked at the thermometer in the hall and it read 14°C.
It occurred to me that every time I could remember in the last three years, that thermometer has read 14°C.
So I put it in some warm water, then some cold, and the reading changed.
Given that I only look at the thermometer to see if it's cold enough to turn the heating on (we don't have a thermostat), it must be that I only wonder whether it's cold enough to turn the heating on at 14°C - I suppose that if it's any colder, I don't bother looking before I turn it on, and if it's any warmer I don't care.