In recent years, the advancements on computational methods and manufacturing technologies have challenged engineers to seek a new class of materials that meet the design challenges that conventional materials are often no longer sufficient to fulfil. The design of smart materials or metamaterials has gained considerable attention owing to their distinctive characteristics and prospective uses. Typically, the metamaterials are porous composite materials consisting of a periodic microstructure, that can be systematically designed by Topology Optimization (TO) [1]. The optimal design of metamaterials, in contrast to empirical approaches seen in the literature, allows for tailored mechanical and thermal behaviours, such as negative indexes on mechanical and thermal properties, with applications ranging from aerospace to biomechanics fields. In the present framework, Asymptotic Homogenization (AH) techniques, along with multi-material TO, are used to design optimal thermoelastic metamaterials. The AH theory assumes periodicity of the microscale (i.e., unit cell), that it is infinitesimally small in comparison to the macroscale (i.e., material). However, in practice the composite material will only encompass a finite number of repetitions. To assess the feasibility of optimal metamaterials in engineering practice, it is crucial to investigate the proximity of the equivalent thermoelastic properties predicted by the AH to those exhibited by real composites [2]. Here, the Representative Volume Element (RVE) method is used to predict the apparent thermoelastic properties of the metamaterial. This involves considering, an increasing number of repetitions of the unit cell and applying homogeneous Dirichlet Boundary Conditions (BC’s) in the RVE. This study introduces a class of optimal metamaterials designed to unlock their potential, employing the AH approach along with multi-material TO techniques. Furthermore, it provides a comprehensive analysis of how the effective properties of those materials are affected in the context of real composites, validating the theoretical approach.