In the present paper, we propose a new FFT based numerical homogenization method to compute the effective conductivity of fractured media involving insulating and superconductive cracks. The governing Lippmann Schwinger (LS) equations based on temperature jump and heat flux jump distribution localized on crack lines are formulated and the geometry of sharp cracks is described by exact expression of form factors. To solve the LS equations, the bi conjugate gradient stabilized method is used and leads to fast convergence. Numerical examples in 2D and 3D show a good accuracy when compared with standard Finite Element Method solutions.