  We report a detailed analytic and numerical study of electronic thermal
conductivity in d-wave superconductors. We compare theory of the cross over at
low temperatures from T-dependence to T^3-dependence for increasing temperature
with recent experiments on YBCO in zero magnetic field for temperatures from
0.04K to 0.4K by Hill et al., Phys. Rev. Lett. 92, 027001 (2004). Transport
theory, including impurity scattering and inelastic scattering within strong
coupling superconductivity, can consistently fit the temperature dependence of
the data in the lower half of the temperature regime. We discuss the conditions
under which we expect power-law dependences over wide temperature intervals.
