On my 25 year old boiler the overrun is controlled by a micro-switch which in turn is switched on/off mechanically by a (bi??) metal arm attached to the water temperature sensor. After around 15 years the overrun started cutting out too early, just after the boiler stopped heating. Easily fixed by adjusting the screw on the metal arm so that the micro-switch again operated when the water was still hot.
My (I guess) 1986 (still going strong, but probably not very efficient) Thorn Apollo has one, but I don't know if it's still contributing to the overall heating effort. Perhaps I'll notice if/when it breaks?
I built one for my BE boiler in the '70s. To get the heat out of its cast iron heat exchanger to where it was most needed.
Most stats are dry no-volt contact types (including electronic ones which typically have an output relay which you can hear as it goes "click").
Heating systems quite often end up with control elements wired in parallel, eg frost stats so it's not uncommon.
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