A dung bath uses biology rather than fire as its heat source. Fresh manure packed together supports a dense population of microorganisms that break down its organic matter, and that breakdown process releases heat as a byproduct, the same way a compost heap or a haystack can grow noticeably warm from the inside out with no external heat source at all.
A vessel, typically sealed to keep its contents from evaporating or being contaminated, was buried into a deep bed of fresh manure packed into a container or pit, and the fermenting material around it held a gentle warmth, usually well below body heat and far below boiling, for as long as the manure kept fermenting, which could be days to several weeks if the bed was large and fresh enough. That made it suited specifically to digestion, an operation meant to proceed extremely slowly at a very low, steady temperature rather than to boil, distill, or calcine anything, and alchemical texts describe replenishing or refreshing the manure bed periodically to keep the fermentation, and therefore the heat, going for as long as the operation required. Unlike a fire-based bath, a dung bath needed no tending of flame at all, only occasional attention to the manure itself.