Homogeneous heat conduction can be easily analyzed by the boundary element method. However, domain integrals are generally necessary to solve the heat conduction problem in non-homogeneous and functionally gradient materials. This paper shows that the three-dimensional heat conduction problem in non-homogeneous and functionally gradient materials can be solved approximately without the use of a domain integral by the triple-reciprocity boundary element method. In this method, the distribution of domain effects is interpolated using integral equations. A new computer program is developed and applied to several problems. (C) 2014 Elsevier Ltd. All rights reserved.