Duplicate Content While Re-Themeing a Site SEO

Hi, I recently migrated a large site for a client from his current hosting company to a new hosting company, but I put the migrated site under a new url and I am goign to put a new theme on it while it is under the new url. Once I have finished, then I keep it with its new hosting company, but put it back under its original url. I have been hearing alot about google and duplicate content.

Will the fact that I currently have a copy of the original site under a new url while I re-theme it for a month become an issue for SEO?

If so, what should I do to avoid this? should I remove the google sitemap or the google # for now?

Its already been sitting there for a week while I research a few things, I plan to start the re-theme this weekend.