In this paper, the heat conductivity of two-dimensional (2D) material containing arbitrary shape pore with highly conducting pore boundary are considered. To model the distinct heat transfer behavior of the pore boundary, the line conduction model is used. The heterogeneity problem of a single void embedded in an infinite matrix is then investigated and solved with the complex variable and the Conformal Mapping techniques. The results of the latter are then used to obtain the effective heat conductivity of the porous material with different homogenization schemes.