Many, forum members, probably the majority of central heat coal burners use a boiler instead of a furnace. The boiler utilizes a water to air heat exchanger installed in the ductwork of the furnace, and this heats the air.
A boiler can supply unlimited or almost unlimited domestic hot water, a furnace can use a dhw loop, but it is not a high volume DHW heater.
And, what happens when the T'stat has called for heat, the stoker fire has increased in size, burning more coal, and then the T'stat is satisfied?? with a gas or oil furnace the flame shuts off, and you have no over-run of heat. But with a coal stoker, the fuel is still burning, not as vigorously, since the comustion fan has shut down, but there is considerable coal still burning on the grate, and this heat has to go somewhere, with a furnace some goes into the ductwork, but most gets wasted, it's pulled up the chimney..
But with a coal boiler, this heat is absorbed by the water jacket, and most is available for the next call for heat, so the boiler is a more effecient heating device.
Just food for thought.