  We present the results of a microscopic calculation of the longitudinal
thermal conductivity of quasiparticles, $\kappa_{xx}$, in a 2D d-wave
superconductor in the vortex state. Our approach takes into account both
impurity scattering and a contribution to the thermal transport lifetime due to
the scattering of quasiparticles off of vortices. We compare the results with
the experimental measurements on high-T$_c$ cuprates and organic
superconductors.
