Brian, No and Stainless steel, copper is not a good metal for this (1) It's too conductive, conducting heat direct too the cold end rather than to the air in the hot end. (2) It oxidizes and flacks on the inside.
I'm not too sure, but is the displacer on this motor also made of glass normally, if so this can also be made of Stainless.
This little motor has a hot end made from the steel case of an AA size NiCad battery.
Ian S C