Unfortunately not in the user interface.
The originating template is a property of the doucment (obviously--that's how it remembers where it came from) and that can be accessed programatically.
You'll need to code such that you "grab" onto the documents, iterate through each one, and use this line
ActiveDocument.AttachedTemplate = "C:\Templates\Letter.dot"
to attache the appropriate template. Then save the doc.
Dan Holme
Office & SharePoint Pro Community Leader
MVP (Windows Server - Directory Services)