The Fourier Transform method is used to solve frequency dependent heat transfer problems. The periodic Lippmann-Schwinger (LS) integral equation in Fourier space with source term is first formulated using discrete Green operators and modified wavevectors which can then be solved by iteration schemes. The objective is to solve the local problem involving strong contrast heterogeneous conductive material, with application to gas-filled porous media with both perfect and imperfect Kapitza boundary conditions at the bi-material interface. The effective parameters such as the dynamic conductivity and the thermal permeability in the acoustics of porous media are also derived from the cell solution. Numerical examples show that the schemes converge fast and yield accurate results when compared with analytical solution for benchmark problems. The formulation of the method is built using static or dynamic Green operators and can be applied to pixelized microstructure issued from tomography images.