  We propose a new theoretical approach to analyze the experimental data for
thermal conductivity of single-grain $i$-AlPdMn quasicrystals. The
interpretation is based on the picture where cluster interfaces are the main
source of phonon scattering at low temperatures. The scattering due to strain
fields of cluster interface is considered in terms of finite dislocation wall
or, equivalently, wedge disclination dipole. Our numerical calculations show
that experimentally observed thermal conductivity in a wide temperature range
can be well fitted by a combination of wedge discliantion dipole scattering and
quasiumklapp scattering processes.
