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"I don't think we can use this by default, or it will break the expected semantics of temporary files under Unix (visible by other processes)."
I proposed to change TemporaryFile, not NamedTemporaryFile. Do you mean that other processes are supposed to have access to the temporary file descriptor? Access through /proc/pid/fd/<tmp_fd>?
O_TMPFILE should increase the security because there is no more race condition between os.open() and os.unlink() (window where an attack can access the file).
My patch uses O_EXCL. It makes possible to use linkat() to create a path for the temporary file (I didn't try it, but I read that it's possible). I don't know if using O_EXCL should be the default.