You can't change the template after the fact because a template is a just starter drawing. But you can change the sheet format which is where the border and title block should be. Go to Properties of the sheet and select a different one.
Keep in mind that if you have custom properties set up, as in populating the title block, you need to pay attention. Any properties that the other sheet format has that you already have a value in, that value will remain. Any properties that the other sheet format has that you don't already have in your drawing, it will add that property and its value. This is handy when you want to bring in "default" values - just delete the existing drawing properties and let the sheet format bring in the defaults.