The Fourier series method is used to solve the periodic homogenization problem for conductive materials containing voids. The problems involving voids are special cases of infinite contrast whose full field solution is not unique, causing convergence issues when iteration schemes are used. In this paper, we reformulate the problem based on the temperature field in the skeleton and derive an equation where the temperature field is connected to values on the pore boundary. Iteration schemes based on the new equation show that the convergence is fast, yielding good results both in terms of local fields and effective conductive properties.