Someone is confused, and it might be me. The Rumford fireplace basically is a set of specifications on fireplace design that was originated by Count Rumford to end the interior smoking, poor burning and therefore poor heating properties of then contemporary fireplaces. Width, height, and depth ratios, plus design of the throat and smoke chamber, are the essence of the Rumford design. Air control is by means of a damper.
That said, a Rumford fireplace will never produce the heat per pound of wood that a modern EPA woodstove produces. The Rumford will draw far more air from the heated space to assure good combustion and no smoking than will a wood stove, and all that air must be replaced from an outside air source -- thus, drawing in large quantities of cold outside air. The Rumford will have a net heat gain, but it will be far less than a wood stove, which has a much lower air draw.
I'm not being critical of anyone who wants a fireplace. But if the choice is for a Rumford fireplace for the primary purpose of heating, there are far better wood burning choices available than a Rumford fireplace.
Incidentally, many years ago I was involved in litigation over a fireplace which smoked into the living space. The homeowner won the case against the fireplace builder because the builder did not follow the Rumford design principles. I'm not aware that anyone has improved upon the design concepts of Count Rumford for a traditional wood burning fireplace.