  Near-field (NF) radiative heat transfer (RHT) over vacuum space between
closely spaced bodies can exceed the Planck far-field (FF) values by orders of
magnitude. Strong effect of superconductivity on NF RHT between plane-parallel
thin-film surfaces of niobium (Nb) was recently discovered and discussed in a
short paper [Kr\'al\'ik et al., Phys. Rev. B 95, 060503 (2017)]. We present
here an extensive set of experimental results on NF as well as FF RHT for
geometrically identical samples made of niobium nitride (NbN), including a
detailed discussion of the experimental setup and errors. The results with NbN
show more precise agreement with theory than the original experiments with Nb.
We observed a steep decrease of the heat flux at the transition to
superconductivity when the colder sample (absorber) passed from normal to
superconducting (SC) state ($T_c \approx 15.2$ K), corresponding to up to an
8-fold contrast between the normal and SC states. This differs dramatically
from the situation in the FF regime, where only a weak effect of
superconductivity was observed. Surprisingly, the contrast remains sizeable
even at high temperatures of the hot sample (radiator) with the characteristic
energy of radiation far above the SC energy gap. We explain the maximum of
contrast in heat flux between the normal and SC states, found at a distance
about ten times shorter than the crossover distance between NF and FF heat
flux, being $d \approx 1000/T$ [${\mu}$m]. We analyze in detail the roles of
transversal electric (TE) and magnetic (TM) modes in the steep decrease of heat
flux below the SC critical temperature and the subsequent flux saturation at
low temperatures. Interestingly, we expose experimentally for the first time
the effect of destructive interference of FF thermal radiation in the vacuum
gap, which was observable at temperatures below the absorber superconducting
transition.
