Oxygen-free copper is an integral part of electric vehicles and renewable energy initiatives as the key conductor material owing to its high conductive properties. However, the poor heat resistance and poor stress relaxation resistance characteristics pose challenges for applications involving heat. This study aims to explore the potential for developing a new pure copper material with enhanced heat resistance and stress relaxation resistance characteristics while maintaining conductivity. Trace amounts of solute elements Mg, Sn, P, Ti, and Ag were added to oxygen-free copper, and the following results were obtained from the cold-rolled material:(1) Mg, Sn, P, Ti, or Ag addition below 500 at ppm has little effect on yield strength.(2) Mg or Ag addition below 200 at ppm has little effect on electrical conductivity.(3) Mg or Sn addition above 100 at ppm increases the half-softening temperature to over 573 K.(4) Mg, Sn, or Ag addition above 100 at ppm increases the residual stress ratio to over 60%.(5) Mg or Ag addition yields a superior balance of electrical conductivity, half-softening temperature, and residual stress ratio; particularly, Mg addition between 100 and 200 at ppm results in an excellent balance.