How to update a customed theme to a new version?

For default WordPress theme the auto update button is there when a new version is available.

But for custom theme’s that option is not available. Is there an easy way to update to a newer version without having to go back and edit any of the customized php files, css files, ect?

I’m trying to make an update to a geoplace theme but there are so many edits already from the old version that would take a lot of time editing the new version.