  The phonon contribution to the thermal conductivity at low temperature in
superconductors with line nodes is calculated assuming that scattering by both
nodal quasiparticles and the sample boundaries is significant. It is determined
that, within the regime in which the quasiparticles are in the universal limit
and the phonon attenuation is in the hydrodynamic limit, there exists a wide
temperature range over which the phonon thermal conductivity varies as $T^2$.
This behaviour comes from the fact that transverse phonons propagating along
certain directions do not interact with nodal quasiparticles and is thus found
to be required by the symmetry of the crystal and the superconducting gap,
independent of the model used for the electron-phonon interaction. The
$T^2$-dependence of the phonon thermal conductivity occurs over a well-defined
intermediate temperature range: at higher $T$ the temperature-dependence is
found to be linear while at lower $T$ the usual $T^3$ (boundary-limited)
behaviour is recovered. Results are compared to recent measurements of the
thermal conductivity of Tl2201, and are shown to be consistent with the data.
