We have found for the first time the reentrant lamellar/onion (lamellar-onion-lamellar) transition with varying temperature under constant shear rate by using simultaneous measurements of shear stress and small-angle X-ray scattering (Rheo-SAXS) for a nonionic surfactant (C14E5)/water system, which exhibits the lamellar phase in a wide temperature range from 15-75 degrees C. The onion state exists in a closed region in the temperature-concentration diagram at a constant shear rate. Temperature-dependence of the lamellar repeat distance (d) at rest has also been measured at several concentrations. It is shown that the increase of d with increasing temperature is necessary for the existence of the lower transition. We have investigated the change in the lamellar orientation in the lamellar-to-onion and onion-to-lamellar transition processes near the upper and lower transition temperatures. For all four kinds of transition processes, the following change in the lamellar orientation is observed; lamellar state (oriented to the velocity gradient direction) <-> further enhancement of the orientation to the velocity gradient direction <-> enhancement of the orientation to the neutral direction <-> onion state.