We present the results of a microscopic calculation of the longitudinal the
rmal conductivity of quasiparticles, kappa (xx), in a 2D d-wave superconduc
tor in the vortex state. Our approach takes into account both impurity scat
tering and a contribution to the thermal transport lifetime due to the scat
tering of quasiparticles off of vortices. We compare the results with the e
xperimental measurements on high-T-c cuprates and organic superconductors.