Low Temperature Thermal Transport in High Temperature Superconducting   BSCCO via Y-doped Insulating Analogue
  In order to separate electronic and phonon mechanisms of thermal transport in high temperature superconducting Bi2212, we measured thermal conductivity of single crystals of Y-doped Bi2212, an insulating analogue of pure Bi2212, in the temperature range between 40 mK and 2 K. Temperature dependence of the thermal conductivity of insulating samples changes from T$^{1.7}$ between 1 and 2 K to $T^{2.6}$ below 200 mK, indicating saturation of the phonon mean free path with decreasing temperature. Overall, thermal conductivity of the insulating samples (which is due entirely to phonons) is strongly suppressed in comparison to that of the superconducting samples. Therefore, a large (and at the lowest temperatures, predominant) part of the total thermal transport in superconducting Bi2212 is due to electrons. 
R. Movshovich, E. G. Moshopoulou, M. Jaime, M. F. Hundley, and J. L.   Sarrao