  We investigate thermal properties of a NbN single-photon detector capable of
unit internal detection efficiency. Using an independent calibration of the
coupling losses we determine the absolute optical power absorbed by the NbN
film and, via a resistive superconductor thermometry, the thermal resistance
Z(T) of the NbN film in dependence of temperature. In principle, this approach
permits a simultaneous measurement of the electron-phonon and phonon-escape
contributions to the energy relaxation, which in our case is ambiguous for
their similar temperature dependencies. We analyze the Z(T) within the
two-temperature model and impose an upper bound on the ratio of electron and
phonon heat capacities in NbN, which is surprisingly close to a recent
theoretical lower bound for the same quantity in similar devices.
