A method for establishing fundamental solutions of general variable coefficient heat conduction problems in anisotropic media using the boundary element method was presented. The pure boundary integral equation is derived for solving general two- and three- dimensional steady heat conduction problems in anisotropic media. The established fundamental solutions are suitable for the situation that the thermal conductivity is a function of spatial coordinates

and therefore the developed integral equation can be used to solve the heterogeneous material heat transfer problems. The domain integrals induced by heat sources can be transformed into a boundary integral using the radial integral method

so a pure boundary element method which does not need any interior points is formed. Three examples for two- and three- dimensional problems are provided and the correctness and effectiveness of the proposed method is validated by comparing the results using the current method with that of using finite element method.