C Ann, I know you have a lot of research books on the Amish, but there's a lot more to them than that. I work with them daily and I can assure you that in the summer, they do wear short sleeves. Maybe not the really low order ones, but the newer order sure do. You can't take something from a book and apply it to ALL Amish, there are countless orders, each with a different set of rules.
As for the fireplaces, they never claimed to make the "heater" part of them, but the wooden mantles, or cases, are indeed made by the Amish in Holmes County, Ohio. I personally know one of the manufacturers of these. As for the pictures you posted, of course they're not of the real Amish who make them as they wouldn't want their pictures taken, so those are "models" of Amish men.