Cessiphus, it has been a while since I've read Nietzsche, but doesn't he attempt to claim in The Gay Science that:
-Energy is limited
-Energy is eternally active, but it can not create new forms
-Time is unlimited
-Space is unlimited
-Therefore energy, in its various manifestations, must repeat itself.
...That might have been in The Will to Power, though, with The Gay Science containing only a parable.
Anyway, he elucidates much further in TWTP. In Section 1063 thereof, Nietzsche states: "The law of the conservation of energy demands eternal recurrence."
And Hiedegger, as I mentioned, wrote a great deal on the subject & Nietzsche's attempted proofs.