Hi not really a WordPress question. Google has a Search Console which you can use to do some on these things. https://search.google.com/search-console/about
If you still can ‘verify’ the live-website version then you can use the domain migration.
Otherwise, manke sure Google has all access to the new domain and wait for Google to learn about the new and forget the temp one.
Oh i see, thought it´s something i´d have to set up on wordpress, or my host (or both). Thank you for your answer, i much appreciate it and i´ll check it out.
