The optimization of structure and thermal properties in 3D-printed insulation materials remains an underexplored area in the literature. This study aims to address this gap by investigating the impact of 3D printing on the thermal properties of manufactured cellular composites. The materials studied were closed-cell foams with a complex cell structure based on the Voronoi cell model, manufactured using incremental technology (3D printing). The influence of the cellular structure of the composite, the type of material used, and the number of layers in the composite structure on its thermal properties, i.e., thermal conductivity coefficient, thermal resistance, and coefficient of heat transfer, was analyzed. Samples of different types of thermosetting resins, characterized by different values of emissivity coefficient, were analyzed. It was shown that both the type of material, the number of layers of the composite, and the number of pores in its structure significantly affect its thermal insulating properties. Thermal conductivity and permeability depended on the number of layers and decreased up to 30% as the number of layers increased from one to four, while thermal resistance increased to 35%. The results indicate that material structure is key in regulating thermal conduction. Controlling the number of cells in a given volume of composite (and thus the size of the air cells) and the number of layers in the composite can be an effective tool in designing materials with high insulation performance. Among the prototype composites produced, the best thermal performance was that of the metalized four-layer cellular composites (λ = 0.035 ± 0.002 W/m·K, Rc = 1.15 ± 0.02 K·m2/W, U = 0.76 ± 0.01 W/m2·K).