Thermal conductivity kappa(xx)(T) under a field is calculated by using a microscopic theory based on Bogoliubov-de Gennes equation for describing vortices and linear response theory. Superconductors with d(x2-y2)-wave and s-wave pairings are comparatively studied, modeled by a tight-binding extended Hubbard Hamiltonian in two spatial dimensions. The whole T-dependence of kappa(xx)(T) is calculated and shows the characteristic T-linear behavior in the lower T. This behavior is analyzed by examining the spatially resolved thermal flow patterns around a vortex. (C) 2002 Elsevier Science B.V. All rights reserved.