To achieve a 20 Gbps data rate using the upcoming 5G communication standard, it is crucial to recognize a domain wall (DW) velocity (v_DW) of 1200 m s⁻¹. We demonstrate a potential means of achieving the DW speed of 1200 m s⁻¹ at low current density in a wide temperature range from 270 to 350 K in Fe-rich GdFeCo magnetic wire. We show a significant relationship between the v_DW and the pulse duration width, which corresponds to the Joule heating effect and the shape of the DW. Generally, if the current density is constant, the current-driven DW displacement is proportional to the pulse width, so the DW speed is also constant. We found that the v_DW increases with the shortening of the applied pulse current width. However, the DW shape appears rounded in the case of long pulse duration width. Accordingly, the damping-like effective field and the Neel DW are not orthogonal to each other except in the wire center; as the efficiency of SOT decreases, the DW speed reduces. We also measured the Dzyaloshinskii–Moriya interaction (DMI) field for 3 ns 30 ns pulse duration widths. In the case of 30 ns, the DMI field was found halved in comparison to the 3 ns width. Generally, the DMI field is a material-specific parameter, and this difference is clarified by the shape of the DW driven by the current. Our findings on the fast and high thermal stability of DW motion at low current density in compensated ferrimagnetic material open new opportunities for high-speed spintronic devices.