Twisting is an important process in the manufacture yarns for textiles and has an influence on woven fabrics, knitted fabrics, and braided fabrics made with such yarns. This study aims to determine how twist coefficients and thermal treatment temperatures influence tensile strength, elongation, and elastic properties of the resulting wrapped yarns. Polyester (PET) yarns and spandex fibers were twisted into PET/PET wrapped yarns and PET/spandex wrapped yarns, and during the process the thermal treatment temperatures as well as twist coefficients controlled by rotor speed were changed. The results show that variations in twist coefficient do not influence the tensile strength and elongation of the PET/PET wrapped yarns. However, an increase in twist coefficient results in an increase in tensile strength and a decrease in elongation of PET/spandex wrapped yarns. The elongation of PET/spandex wrapped yarns thermally treated at 160℃ is lower than that of untreated PET/spandex wrapped yarns by 86%. In addition, the residual stress and permanent deformation of PET/spandex wrapped yarns both decrease as a result of the increasing thermal treatment temperature.