In A15 superconducting wires, it is known that the critical current has a dependence on the strain in a magnetic field. Therefore, RHQ-Nb3Al wires are being studied to develop a high field magnet. Since the wire is usually composed of three or more materials, residual strain is induced by the different coefficients of thermal expansion in the materials in the cooling process after A15 phase transformation. In neutron diffraction measurements at room temperature, we previously reported that the residual strain of Nb3Al filaments in the wire is tensile. We also reported that the difference of the residual strain in Nb3Al filaments, as obtained at room temperature, has an effect on the tensile strain dependence of the critical current. In this study, we effectively reduced the residual strain by using a thermal cycle method after A15 phase transformation. By applying one thermal cycle process, the tensile residual strain was decreased by approximately 0.08%. This is the first investigation of the thermal cycle effect on the residual strain in the RHQ-Nb3Al wire. Studies on the thermal cycle are necessary to understand the mechanical properties of the wire. In this paper, we report the details of the thermal cycle method, its effect on the lattice structures of Nb3Al and Cu at room temperature, and the analysis results from the perspective of material strength in strain recovery and its hysteresis.