  Thermal conductivity $\kappa_{xx}(T)$ under a field is investigated in
$d_{x^2-y^2}$-wave superconductors and isotropic s-wave superconductors by the
linear response theory, using a microscopic wave function of the vortex lattice
states. To study the origin of the different field dependence of
$\kappa_{xx}(T)$ between higher and lower temperature regions, we analyze the
spatially-resolved thermal conductivity around a vortex at each temperature,
which is related to the spectrum of the local density of states. We also
discuss the electric conductivity in the same formulation for a comparison.
