How to protect the copyright of the thesis draft?
If you live in the US or any other country that observes the rules of the Berne Convention, your work is automatically protected by copyright as soon as it is saved to a fixed medium (which may be your hard drive, a printout, or scribbles in a notebook). 

So if your work is written down, it's already protected with respect to copyright.

There may be other things about the draft that you wish to protect - for example, you may wish to ask the proofreader not to speak about your ideas with anyone else - but that is not a copyright issue.