  The thermal conductivity $\kappa$ is calculated for the Abrikosov vortex
lattice with d-wave pairing. The Andreev scattering rate arises from the self
energy term in Gorkov's integral equation for the corresponding Green's
function. The impurity scattering rate is calculated self-consistently from
this Green's function in the t-matrix approximation. Neither point-like
impurity scattering with a phase shift in the almost unitary limit nor in the
Born limit can consistently explain recent zero-field and finite-field
measurements of $\kappa/T$ at low $T$ in ultraclean YBCO. Our theory also
applies to the spin triplet pairing states with vertical or horizontal line
nodes in Sr$_2$RuO$_4$
