  The search for strategies to harness the temperature of quantum systems is
one of the main goals in quantum thermodynamics. Here we study the dynamics of
a system made of a pair of quantum harmonic oscillators, represented by
single-mode cavity fields, interacting with a thermally excited beam of
phaseonium atoms, which act as ancillas. The two cavities are arranged in a
cascade configuration, so that the second cavity interacts with phaseonium
atoms only after their interaction with the first one. We provide exact closed
dynamics of the first cavity for arbitrarily long interaction times. We
highlight the role played by the characteristic coherence phase of phaseonium
atoms in determining the steady states of the cavity fields as well as that of
the ancillas. Also, we show how the second cavity follows a non-Markovian
evolution due to interactions with the "used" ancillary atoms, that enables
information exchange with the first cavity. Adjusting the parameters of the
phaseonium atoms, we can determine the final stable temperature reached by the
cavities. In this way, the cavities can be heated up as well as cooled down.
These results provide useful insights towards the use of different types of
ancillas for thermodynamic cycles in cavity QED scenarios.
