I think that extant boiling coppers and rocket stoves have a lot in common. Here’s the description of how boiling coppers/furnaces work from “Cooking and Dining in Medieval England” by Peter Brears (p155, 156):
The actual furnaces have an almost hourglass section, the bottom half containing the burning logs and faggots in its combustion chamber. The flames were then constricted, to emerge as a strong, vertical blast directly under the convex base of the boiler mounted above, the bowl shaped upper section of the furnace keeping the flames just a few inches from the boiler’s sides, before the passed up the flue.
The surviving furnaces at Warkworth, Ashby de la Zouch and a number other castles all adopt a common form, having a cylindrical interior with a ledge some 30 inches from ground level, an arched fireplace facing into the side of the adjacent hearth, and an enclosed space above, with a vent leading either to the open air or to the upper part of the main chimney.
Once a large pot and been suspended inside, and its rim sealed to the inner ledge with mortar and sheet lead, this type of furnace could be fired like a bread oven, burning faggots being thrust to the back of its firing chamber, so that the flames would pass beneath and around the pot, before emerging from the top of the fireplace arch and ascending the main chimney. This ensured that as much of their heat as possible was transferred to the pot, rather than being lost to the open air.
In a later development, the fireplace was still located in the side-wall of the hearth, but the flames were now conducted backwards under the bottom of the boiler, around a baffle, and then forwards around both the upper sides of the boiler to a chimney directly above the fireplace. This made for a much more efficient use of fuel, since the flame passed twice their former distance around the boiler. This system was later used for most great boiling houses, including those at Hampton Court Palace.
The other place to work out period water heating technology is in brewing;