  We investigate the photon-mediated thermal transport between a
superconducting electrode and a normal metal. When the quasiparticle
contribution can be neglected, the photon-mediated channel becomes an efficient
heat transport relaxation process for the superconductor at low temperatures,
being larger than the intrinsic contribution due to the electron-phonon
interaction. Furthermore, the superconductor-normal metal system acts as a
nearly-perfect thermal diode, with a rectification factor up to $10^8$ for a
realistic aluminum superconducting island. The rectification factor can be also
tuned in a phase-controlled fashion through a non-galvanic coupling, realized
by changing the magnetic flux piercing a superconducting quantum interference
device (SQUID), which modifies the coupling impedance between the
superconductor and the normal metal. The scheme can be exploited for passive
cooling in superconducting quantum circuits by transferring heat toward normal
metallic pads where it dissipates more efficiently or for more general thermal
management purposes.
