Ironmaking from Medieval Europe to Colonial America

What was the medieval technology of ironmaking that came to America? After all, to speak of those times spans over 500 years -- something must have changed. It seems to have been the charcoal fueled, cold blast furnace, apparently developed several places, perhaps independently. China, India, Spain, Sweden, and Britain that made the transition. Certainly it had some small improvements, but continued until displaced by the Bessemer system in the 19th century, and even then some smaller iron furnaces in America continued with the same technology plus small adaptations. Even when new furnaces were built, they were sometimes still a cold air, charcoal fueled blast furnace not unlike those of 14th century Europe. The only apparent new thing was the an attempt to introduce a hot blast, although this was not always accomplished - and some places still adamantly clung to the cold blast system, until well after it was conclusively shown that hot blast made better iron.

Given that the Medieval Technology evolved over a long time span and across continents it seems clear that in the new world the medieval technology lingered, even as new experiments leading to a new technology were catching on.