Would work, but has some side-effects, e.g. that it doesn't work when you log on to SharePoint with another user, than the one you are logged on to Windows.
But I found a solution: I create a WebPart with SharePoint-Designer, which creates a link to the _layouts/download.aspx-page with the parameter SourceURL pointing to the word file. This way, the file is downloaded and open locally, with the effect, that Word creates a new document of the template.