Can a hotter bath sometimes better preserve a quantum battery?

A framework for how multi-level quantum systems lose energy to a heat bath shows that the amount of useful work a qudit can deliver is not a simple function of bath temperature — sometimes a hotter environment degrades it less. Even stranger, repeatedly applying the channel can cause work-extraction measures at different temperatures to cross, a quantum analogue of the Mpemba effect, where hot water freezes faster than cold.