Hello,
Thank you for your question regarding temporarily making a site private. You can easily password protect the directory that stores your files. This will allow your site to be accessible only to people who have the login info.
For example, you can password protect the document root of the website you want to make private.
Alternately, if you are using a CMS (such as WordPress, Joomla, Drupal) you can use a plugin or extension to password protect the site, or put it in maintenance mode.
Thank you,
John-Paul