In the olde days when fuel was cheap, the thermostat would shut down the fire and circulator at the set temperature so there was little overshoot. That wasted a whole lot of heat that was in the boiler, and would just drift up the chimney. So common practice became to keep the circulator running to dump that heat into the living space instead.
With big olde boilers that could be several degrees of overshoot, I lived one place where it would overshoot five degrees. But newer smaller boilers, usually only overshoot a couple degrees.
Having a thermostat that can predict that, so it hits the right temperature at the right time, is the cat's ass.
