Yes, sorry. I was thinking about a superconducting film on, say, a silicon substrate. Me and some colleagues were discussing the thermal conductivity of superconductors at mK temperatures, and it was stated that they do not conduct heat. But I think that's wrong; there is virtually no heat carried by electrons, but it is still carried by phonons, right?
Or maybe phrased slightly differently, if we put a purely superconducting link between a 4K stage and a mK stage, it is not a perfect thermal isolation, right? It's just a rather poor conductor