Nowadays, the growing concern about improving thermal comfort in different structures (textiles, buildings, and pavements, among others) has stimulated research into phase change materials (PCMs). The direct incorporation of PCMs into composite materials can cause mechanical impacts. Therefore, this study focuses on the design of phase change coaxial fibres (PCFs), using commercial cellulose acetate (CA) or recycled CA obtained from cotton fabrics (CAt) as the sheath and polyethylene glycol (PEG) 2000 as the core, via the wet spinning method; the fibres vary in molecular weight, concentration and ejection velocity. The fibres were assessed for their optical, chemical, thermal, and mechanical properties. The presence of PEG2000 is confirmed in the core of the fibres. Thermal analyses revealed a mass loss at high temperatures, attributable to the presence of PEG2000. Notably, the fibres with CA (Mn 30,000) showed superior thermal and mechanical performance. The melting point of PEG2000 incorporated into these PCFs coincided with the melting point of pure PEG2000 (about 55 °C), with a slight deviation, indicating that PCFs were obtained. Finally, the results point to the application of the fibres in civil engineering materials requiring a phase change between 50 and 60 °C, providing promising prospects for their use in applications requiring thermoregulatory properties.