Richard, I think the problem with this is that it spreads the non-portable
or OS-dependent parts of the code over several places rather than
concentrating them all in one place.

After close_without_unlink(), what would happen when the context manager
exits or when the object is garbage collected?  Would it then get unlinked?

My preference would be to specify the behavior of close/__exit__/GC
operations at the time of the NamedTemporaryFile creation, so that the rest
of the code can be left unchanged.