Thanks, that is also what I thought! Colleagues of mine said something about superconductors being poor thermal conductors, which I did not really understand because I thought phonons should just propagate through them. But maybe what they meant is that it is hard to thermalize the electrons in the superconducting material.
For the record, I don't think films are any different than bulk superconductors. Of course the boundaries will affect phonon propagation, but that is not specific to superconductivity.