Developer Tab > Restrict Editing > No Changes (with exceptions)

Select the entire body of the document (template) mark that as an exception.

Apply protection with a password.

You have made it harder to make changes in the header(s) or footer(s) in the document. You can't do it directly within Word. This also means that you cannot change other settings for headers and footers.

Sections / Headers and Footers in Microsoft Word 2007-2013
Making Forms with Microsoft Word

Note: I said "make it more difficult" not "stop." I know of know way to let someone see something and prevent them from copying what they see. Computers make it easier, but a pencil and paper in the hands of someone good will do.

There is an old saying that locks help keep honest people honest. While I know of no way to directly edit such a document header/footer that does not mean that there is no way.