\documentstyle{article} \begin{document} A current damaged configuration ${\rm B_t}$ and the corresponding fictitious undamaged configuration ${\rm B_f}$ of a Representative Volume Element (RVE) characterized by a second rank anisotropic damage tensor $D_{ij}$ are first postulated. \par Then, by taking account of the effective undamaged surface element of ${\rm B_f} $, the heat flux vector $q^C_i$ due to heat conduction in ${\rm B_t}$ is formulated. The heat flux $q^R_i$ through cavities is also formulated by calculating the gray-body radiation through a row of cavities in RVE of ${\rm B_t}$. \par The heat conduction law for overall heat flux $q_i = q^C_i +q^R_i$ and the equation of heat conduction in anisotropically damaged materials are expressed by defining the equivalent thermal conductivity tensor $L^{EQ}_{ij}$ in the damaged material. \par The tensorial nature of the resulting equations and the variation of $L^{EQ}_ {ij}$ due to the development of anisotropic damage $D_{ij}$ are discussed. Finally, the resulting equations are applied to the analysis of anisotropic creep damage problems under thermo-mechanical loading. \end{document}