  We investigate the heat transport properties of a three-level system coupled
to three thermal baths, assuming a model based on superconducting circuit
implementations. The system-bath coupling is mediated by resonators which serve
as frequency filters for the different qutrit transitions. Taking into account
the finite quality factors of the resonators, we find thermal rectification and
circulation effects not expected in configurations with perfectly-filtered
couplings. Heat leakage in off-resonant transitions can be exploited to make
the system work as an ideal diode where heat flows in the same direction
between two baths irrespective of the sign of the temperature difference, as
well as a perfect heat circulator whose state is phase-reversible.
