Abstract: Here we report on the development of NbN/SiNx:H/SiO2-membrane structures for investigation of the thermal transport at low temperatures. Thin NbN films are known to be in the regime of a strong electron-phonon coupling, and one can assume that the phononic and electronic baths in the NbN are in local equilibrium. In such case, the cooling of the NbN-based devices strongly depends on acoustic matching to the substrate and substrate thermal characteristics. For the insulating membrane much thicker than the NbN film, our preliminary results demonstrate that the membrane serves as an additional channel for the thermal relaxation of the NbN sample. That implies a negligible role of thermal boundary resistance of the NbN-SiNx:H interface in comparison with the internal thermal resistance of the insulating membrane.