Considering the major role played by sandwich structures in many fields where high stiffness-to-weight ratio is required, the selection of a suitable core material is of paramount importance. In order to face the environmental problems related to waste disposal, the selection of an eco-friendly core material is now included in the design criteria of sandwich structures. Agglomerated cork is recognized as a good solution that combines satisfactory mechanical performances and eco-sustainability. Many research studies individually addressed cork’s morphological, thermal, and mechanical features without providing a comprehensive overview of the relationships that exist between them. In this work, the investigation of the peculiar cork morphology allowed learning more about its good insulation capacity and its impressive recovery capability. The use of dynamic mechanical analysis (DMA) and thermogravimetric analysis (TGA) clarified the influence of temperature on both flexural and compressive performances. The effect of testing parameters such as temperature and speed on agglomerated cork properties was validated through statistical analysis. Moreover, to highlight agglomerated cork advantages and drawbacks, the work provides also a comparison with more traditional polyvinylchloride (PVC) foams commonly used in industrial applications.