  We calculate the electronic thermal conductivity in a d-wave superconductor,
including both the effect of impurity scattering and inelastic scattering by
antiferromagnetic spin fluctuations. We analyze existing experiments,
particularly with regard to the question of the relative importance of
electronic and phononic contributions to the heat current, and to the influence
of disorder on low-temperature properties. We find that phonons dominate heat
transport near T_c, but that electrons are responsible for most of the peak
observed in clean samples, in agreement with a recent analysis of Krishana et
al. In agreement with recent data on YBa_2(Cu_1-xZn_x)_3O_7-\delta the peak
position is found to vary nonmonotonically with disorder.
