Synthetic polymer-based gradient foams have considered as promising category of functionally graded materials with unique properties. In this study, the carbon dioxide (CO₂) foaming technology has used for PET-PEN (Polyethylene Terephthalate - Polyethylene Naphthalate) copolymer towards porous functional materials with thermal insulation with reasonable mechanical strength. Through scanning electron microscope based morphological characterization, a potential to fabricate gradient foam structures with micro-pores has identified. It has shown that variation of post-foaming temperature can tune the pore size distribution although the very high post-foaming temperature tends to cause structural instability. Thermal measurement data set the limits of operation, confirmed by simultaneous differential scanning calorimeter and thermo-gravimetric analysis. Mechanical stress and thermal conductivity also has measured to find rationale of thermal insulation with reasonable mechanical strength and to elucidate the actual 3D grid foam of copolymer.