This work focuses on the evaluation of the effective thermal conductivity of ultra-light materials, as the highly porous two-phase systems (foams). The main aim of the paper is to show that the exact mathematical solution of the heat conduction equation, based on the constitutive Fourier law and without any empirical constant nor ad hoc assumptions, is possible under an assumed thermal condition. To cover the range of real thermal conditions the present theoretical approach employs the two extreme thermal assumptions, i.e. parallel isothermal lines and parallel heat fluxes. The analysis is carried out upon an elementary cubic cell investigating the effect of structure, porosity, saturating fluid and solid material of open-cells foams. Comparisons among the present purely theoretical results and some experimental data of the literature confirm favorably the present approach. (C) 2019 Elsevier Ltd. All rights reserved.