Transport properties of two-dimensional charged bosons in the normal a
nd superconducting state are derived. The Wiedemann-Franz law and the
Lorentz number are obtained for the normal state. A strong suppression
of the quasiparticle scattering rate and a strong enhancement of the
thermal conductivity in the superconducting state are found. Temperatu
re dependence of the in-plane thermal conductivity of YBCO crystals is
explained.