In this paper, we present a boundary-volume based Lippmann Schwinger integral equation for numerical homogenization problems of heterogeneous conductive materials with arbitrary contrast ratio and imperfect interface behavior. It is shown that the interior temperature gradient within each homogeneous phase is connected to the material dissimilarity quantities at all boundaries between different phases. The Kapitza interface model can also be included in the formulation. The basic FFT iteration schemes converge fast even for infinite contrast in the case of usual interface conditions. In the case of Kapitza's interface, Conjugate Gradient schemes based on the new formulation converge fast and yield accurate results when compared with standard Finite Element Method.