  The thermal conductivity of Sr2RuO4 along the least conducting direction
perpendicular to the RuO2 plane has been studied down to 0.3 K. In this
configuration the phonons remain the dominant heat carriers down to the lowest
temperature, and their conductivity in the normal state is determined by the
scattering on conduction electrons. We show that the phonon mean free path in
the superconducting state is sensitive to the density of the quasi-particles in
the bulk. An unusual magnetic field dependence of the phonon thermal
conductivity is ascribed to the anisotropic superconducting gap structure in
Sr2RuO4.
