Materials with engineered micro-structures are still an emerging topic, since they can be optimized for given functionalities, and therefore may exhibit higher performances when compared to standard bulk materials. When used not for mass production, but tuned for on-demand applications, their manufacturing involves prototyping rather than mass-production flows. For instance, 3D printing is one possible candidate, when the micro-structure has not a too small scale length. As a counterpart, there are some uncertainties involved, due to a not-so-well controlled production flow, that should be taken into account for the overall design problem. We also address herein non-conventional cases where transient thermal evolutions leads to a so-called macroscopic memory effect (a non local-in-time model), when microsctructure phases exhibit a large contrast in thermal conductivity,. Concerning optimization of these materials and structures for thermomechanical evolutions, topology optimization is of interest at macroscale, while for ensuring manufacturability, parametric optimization is preferred at the microstructure scale. In this work, we promote non-intrusive strategies, such as probabilistic collocation method, and genetic algorithms for optimization. Since the direct problem is untractable, upscaling techniques are used, herein pseudo-periodic homogenization; concerning design parameter descriptions, we rely on a level-set discretization on a dedicated mesh.