The construction and demolition waste recycling into secondary raw materials is vital to achieving a sustainable and circular building life cycle. Expanded polystyrene (EPS) is one of the materials whose recycling rate should be increased. EPS boards can be shredded and used as aggregate of lightweight cement composites resulting in a material with combined properties subjected from EPS and mineral binder. To reduce the open structure of shredded EPS particles, proper treatment could improve EPS performance. The heat treatment of the aggregates can reduce the volume and increase their density. In this paper, EPS aggregates were heat-treated at 120 and 130 °C, and heat-modified EPS aggregates with a bulk density of 40 and 100 kg/m3 were incorporated as filler material in gypsum composites. The composites’ density, compressive strength, thermal conductivity, and sound absorption were characterized. Results indicate that a composite with a compressive strength from 15 to 136 kPa and a material density ranging from 48 to 194 kg/m3 can be obtained. Thermal conductivity was achieved from 0.0390 to 0.0604 W/(mK). Following the ISO 10534-2 standard, the noise reduction coefficient was determined and showed promising results at 600 to 800 Hz, reaching a sound absorption coefficient of 0.88.