I think an unheated storage space could damage your beautiful table in 2 ways. The unheated units allow more humidity. To me that would be the real danger. Wood glue has been the same for a long time. But there is no way to know what glue has been used. A friend of mine stored a saddle of mine in an unheated unit for a few months. She returned it covered in mold. It is such a beautiful piece that I would not take a chance on it. I would get a heated storage unit.