  For heat engines working between two heat baths, functionality is often
conditioned on a set of fixed constraints such as given internal structure of
the engine and given temperatures for the baths. It is, however, important to
devise heat engines which can function adaptively, in particular when the
engine is a quantum system and the baths are subject to fluctuations. Here we
study a model for an adaptive quantum heat engine whose heat baths can have
variable temperatures. We obtain conditions under which such an engine can
still operate. Moreover, we propose an enhancement of the heat engine by
coupling it with an appropriate controller which changes the internal structure
of the engine. Interestingly, we prove that this enhanced engine can always
operate and we also obtain conditions for maximum power extraction from this
engine for all temperatures of the heat baths.
