Death Of Three Young Ladies Backpacking...
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No best answer has yet been selected by garryjs. Once a best answer has been selected, it will be shown here.
For more on marking an answer as the "Best Answer", please visit our FAQ.I agree with shaunjosh. The problem is likely to be the motor in the divertor valve sticking which gives power to the boiler even when the heating controls are not calling for heat. This usually happens when the system has been on and doesn't go off at the allotted time. Also it can go the other way where the system doesn't turn on. It's annoying problem and as you say will then work fine for a while.
If it does fail completely you can guarantee it will be on the coldest day of the year when the only plumber you can get wants to charge an arm and a leg and can only come out in two weeks
The thermostat may well be a low temperature or froststat designed to override the programmer and maintain a minimum temperature overnight etc. If not, it could be just wired wrongly or badly and picking up a live supply from somewhere. See if the heating works normally through the programmer with this stat turned down low, you may have thermostatic rad valves for general use.
If it were a microswitch sticking you would not be able to turn the heating off by the thermostat which is the next switch after the programmer heating channel and does the same job of controlling the motor valve for heating.