Foamed concretes are highly porous materials with excellent insulation properties. Their thermal conductivity is strongly dependent on the pore structure, characterized by the porosity as well as the shape and size distribution of pores. To define the representative volume element (RVE) of foamed concretes with high fidelity, we develop NRGene, an automatic generator of cubic samples with spherical air inclusions whose number and size obey a given distribution. We compute the effective thermal conductivity tensor for a given RVE using finite-element-based computational homogenization. The hi-fi RVE of foamed concretes may contain hundreds of millions of finite elements, making it better suited for benchmarking than for everyday engineering applications. Then, having the hi-fi model as benchmark, we propose a simplified model consisting of the hi-fi model called with a truncated histogram as input, which is largely cheaper while keeping a satisfactory accuracy. We model 21 different foamed concretes with a wide range of porosities and different compositions of the cement paste. Further, we demonstrate that it is the volume of all the pores of a given size, and not its quantity, what affects the effective thermal conductivity of foamed concretes.