The aim of this experimental investigation was to produce a form-stable phase change material (PCM) able to reduce the need for nonrenewable energy resources required for the heating/cooling of buildings located in regions characterized by different climatic conditions. The innovative PCM must also be sustainable and must be produced according to the principles of the circular economy. To achieve such ambitious goals, a form-stable, sustainable PCM was produced through vacuum impregnation. The form-stable PCM was produced starting from a low-toxicity, low-flammability polyethylene glycol of medium molecular weight (PEG 800), which was included in porous stone granules obtained as waste products of the cutting/processing of local (Lecce) stone. The thermal properties and thermal stability of PEG 800 and of its PCM-composite were evaluated by employing differential scanning calorimetry (DSC) and thermo-gravimetric analysis (TGA). The appropriate parameters to perform the impregnation procedure were identified through rheological and calorimetric analyses. A simple leakage test was performed to assess if the PEG polymer can leak from the stone flakes. Finally, the new PCM was added as an aggregate in aerial-lime-based mortars, and the mortar’s properties were analyzed in fresh (workability) and hardened (flexural and compressive strength and thermal characteristics) states for potential applications, particularly in ancient buildings.