We often spend a few days at the Pacific coast in Seaside, Oregon. There is an historic salt works located in Seaside that was established when the Lewis and Clark expedition set up out there after their journey west in the early 1800's (this is the USA after all, all of our "history" is recent when compared to yours). I suspect this "stove" is a reconstruction since the inside of the firebox looks like concrete.
We were there one weekend when there was a re-enactment taking place out on the dunes near the beach. They had a large fire going and they were boiling seawater to extract the salt.
Very interesting. In Sicily, they had basins near the sea, and as waves washed over the basins and retracted to the sea, salt was left in the basins. I have images of this as well, near to where this picture was taken.