Board Thread:Script Suggestions/@comment-25689316-20161231131325/@comment-26143371-20170114184703

I've never actually tried it with templates, but I think PageRenameAuto-update just works fine with them. According to it's description it "can fix page links and transclusions on other pages when not leaving a redirect" (emphasis mine).

Technically there is no difference between templates and normal articles. Normal pages can be transcluded the same way as templates, it's just something that's rarely done.