The thermomechanical behavior of ethylene–propylene–diene monomer (EPDM) foams filled with different concentrations of a paraffin (melting temperature of 21 °C) are investigated for the first time. Samples were prepared by melt compounding and hot pressing, and the effects of two different foaming agents such as Expancel® 909DU80 (E) and Hostatron® P0168 (H) were investigated. Scanning electron microscopy and density measurements highlighted that the use of E foaming agent led to foams with a closed-cell morphology and a mean pore size of about 20 μm, whereas foams expanded with H were characterized by a mixed closed-/open-cell porosity with a larger cell size (of about 100 μm) and a less uniform pore distribution. Differential scanning calorimetry analysis demonstrated that the produced foams were endowed with noticeable thermal energy storage properties (up to 67 J/g with a paraffin amount of 50 wt%). The corresponding thermal parameters were found in the range of 15–50 J/cm3, which were directly dependent on the paraffin content in both heating and cooling. The drop in the maximum tensile stress at elevated paraffin contents observed in the tensile impact tests at 23 °C was counterbalanced by a noticeable enhancement of the deformation at break and of the absorbed impact energy. Tensile tests performed at 0 °C demonstrated that the addition of paraffin within the foams was responsible for a substantial increase in stiffness, whereas at 40 °C, it plays a plasticizing effect.