This article describes an innovative thermal insulation barrier in the form of a sandwich panel manufactured using 3D FDM printing technology. The internal structure (core structure) of the barrier is based on the Kelvin foam model. This paper presents the influence of the parameters (the height h and the porosity P of a single core cell) of the barrier on its properties (thermal conductivity, thermal resistance, compressive strength, and quasi-static indentation strength). The dominant influence of the porosity of the structure on the determined physical properties of the fabricated samples was demonstrated. The best insulation results were obtained for single-layer composites with a cell height of 4 mm and a porosity of 90%, where the thermal conductivity coefficient was 0.038 W/(m·K) and the thermal resistance 0.537 (m2·K)/W. In contrast, the best compressive strength properties were obtained for the 50% porosity samples and amounted to about 350 MPa, while the moduli for the 90% porosity samples were 14 times lower and amounted to about 26 MPa. The porosity (P) of the composite structure also had a significant effect on the punch shear strength of the samples produced, and the values obtained for the 90% porosity samples did not exceed 1 MPa. In conclusion, the test showed that the resulting 3D cellular composites offer an innovative and environmentally friendly approach to thermal insulation.