This seems ill-advised:

* If a deterministic filename is needed, tempfile probably shouldn't be used.

* Mock objects are typically used when alternative behavior is needed for testing.

* The proposed feature would preclude a possible future development path to use SystemRandom which wouldn't be able to accept a seed.

* Having the same filename used on successive runs will likely cause other problems. Generally, a user of tempname can assume that filename doesn't already exist and the proposed option would undermine that assumption.

* I suspect if there were a real need here, we would have heard about it a long time ago.  This module is over two decades old.