I know you would like simply to install new template on your old site and... boom... got old site with new template. This sounds nice but it's not possible. Why?
Because every Joomla template has different structure, layout of modules, and other elements.
So, after installation of template on the old site, you'd need additional work in Joomla backend to change all elements to make them "fit" into the new template.
HotStart is used to help in building new website. It's unusable for websites already filled up with content.