I bought this place with three Kivas. Not much heat, some smoke. But one was built of brick, so got the best heat out it.
If your kiva smokes at all, IMO lengthen the flue and or reduce the size of the opening.
For heat, for most kivas, IMO a woodstove standing in front of it on a hearth retains the appearance and increases the safety, efficiency, heat and efficiency. You will use less wood to get more heat.
For a brick or adobe kiva IMO a woodstove or insert that fits inside should do well. If you get any smoke, even the smell, insist the installer eliminate it. He should know how to do that. He might straighten out the flue or lengthen it. Just insist on results.
My small jotul inside one Kiva and the large one in front of another can heat 5,000 square feet. They are made of replacable parts -- so it's easy to fix when something goes wrong. (Dual zone heating
)
Good luck and let us know how it comes out.
Last thought -- woodstove or insert inside the kiva might be best if you have small children. You could move the woodstove out iin front later when the kids are older.