The thermal conductivity kappa(chichi) is the difference between higher and lower temperature regions, because the spatially-resolved thermal conductivity kappa(chichi)(r) is localized around the vortex core at lower temperature and delocalized at higher temperature. On one hand, much attention is focused on the spin and charge ordering around the vortex. When the antiferromagnetism appears around the core, the energy gap suppresses the density of states on the Fermi energy, and the zero-energy peak at the vortex core splits or vanishes. The kappa(chichi) under the Neel temperature is suppressed by the antiferromagnetism. We solve the Bogoliubov-de Gennes equation self-consistently by two-dimensional extended Hubbard model including the repulsive interaction U, and calculate the on the basis of the linear response theory. The picture of the spatial variation of the thermal conductivity kappa(r) through the spin resolved local DOS well explains recent experiments. (C) 2004 Elsevier B.V. All rights reserved.