Once the proper domain’s DNS is changed and has propagated, you’ll need to update the site and home URL settings in WP. Avoid using the temp domain elsewhere on the site to minimize what needs to be changed.
If it’s possible to add the domain to your GD account before making DNS changes (it may have already been added during account setup), you could do so now and use your computer’s hosts file to direct domain traffic to the GD server. Then your new site will behave like the DNS has changed already. You will not be able to access the old site if you do this unless you revert the hosts file and restart your computer.
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