But passive cooling reducing power draw is actually wrong. A fan uses almost no energy at all, meanwhile passively cooled, the chip would run hotter, causing it to again draw more power. These chips like being as cool as possible.
You can even get into thermal runaway because of this: too hot > more power draw > gets hotter > even more power draw > even hotter...
It would be underwhelming hash wise, but I suppose you could use the internal temperature sensor on the BM1397 and adjust the hash frequency and core voltage until the miner is stable with whatever passive cooling..