Why is sudoedit writing to a temporary directory?

The point of sudoedit is to allow users to edit files they wouldn’t otherwise be allowed to, while running an unprivileged editor. To make this happen, sudoedit copies the file to be edited to a temporary location, makes it writable by the requesting user, and opens it in the configured editor. That’s why the editor shows an unrelated filename in a temporary directory. When the editor exits, sudoedit checks whether any changes were really made, and copies the changed temporary file back to its original location if necessary.