You don't upload the .dwt files. That's a Dreamweaver Template which is only used by DW.
From the .dwt you create .htm files and upload those.
Yeah, you don't need to upload the .dwt files at all, unless you need to share them with other developers on your site.
They are used locally on your computer by DW to create and maintain your .html files. All you need to upload are the .html files and even
if you do upload the Templates folder and the .dwt files and try and navigate to them in your browser, they will just download rather than display in your borswer. It might even be that your server won't even serve them up so they wouldn't even download. In any event, you won't see them in your browser...but that's ok because you only need to see the .html files that the .dwt files are used to create/maintain.