  Previous experimental studies of the thermal conductivity of plastically
deformed lead crystals in the superconducting state have shown strong anomalies
in the thermal conductivity. Similar effects were also found for the thermal
conductivity of bent ${}^4\text{He}$ samples. Until now, a theoretical
explanation for these results was missing. In this paper we will introduce the
process of phonon-kink scattering and show that it qualitatively explains the
anomalies that experiments had found.
