Quasiparticle thermal conductivity in the vortex state of high-T${}_c$ cuprates

We present the results of a microscopic calculation of the longitudinal thermal conductivity, $\kappa$, of a d-wave superconductor in the mixed state. Our results show an increase in the thermal conductivity with the applied field at low temperatures, and a decrease followed by a nearly field independent $\kappa (H)$ at higher temperatures, in qualitative agreement with the experimental results. We discuss the relationship between the slope of the superconducting gap and the plateau in $\kappa (H)$.