By copying the old template will cause you to loose all the fixes in that template (and there are some), so you could just copy it to different directory and use it before you have all changes implemented. Usually I recommend copying your custom theme into another directory anyway, as it makes things easier.
There are two ways to merge changes. You can either add your own changes to the new version or new version to your own template. Usually I recommend to look file by file which way is the easier and use the shorter road. Some files may be changed only in one source, so those files could just be copied over..
What you need is to have a good diff tool and three template trees:
1) old release without your changes
2) old release with your changes
3) new release without changes
Then you just look changes between:
1) old and new release
2) old and own version
If there are changes only in 1 or 2, just copy that file to the new template.
If there are changes in them both, look which one has less changes and apply those to file based on the another tree.
Usually doing this takes only a few hours -- there are not too many changes in K1.5.7..