The template for the TwitterFeed widget is indeed empty, and this is the correct one. This widget does not use anything from its template. It only generates a script, which calls the Twitter API and embeds what you see on the page, depending on the options. All the user interface is embedded into the page from this script.
The TwitterFeed widget actually combines the different embed codes supplies by twitter (https://twitter.com/about/resources/widgets) into one Sitefinity widget. If you want to control the appearance, you can do so from the widget designer, but there is not Sitefinity template for this control.