We study dilute aqueous solutions of a triblock copolymer PEO-PPO-PEO (Pluronics P84) by rheometry coupled with small-angle light scattering. The zero-shear viscosity increases by 5 orders of magnitude upon increase of temperature from 30 to 40.5 degreesC. This increase can be explained by the growth of spherical micelles to entangled cylindrical aggregates. In the non-Newtonian regime, we find evidence for shear-induced demixing below 37.7 degreesC and for gradient shear banding above this temperature. Thus, above a critical temperature the shear-induced demixing triggered by the flow in the vicinity of the cloud point (43 degreesC) appears linked to a phase separation of regions with different shear rates. At fixed concentration, the control parameters of the dynamic phase diagram are the temperature and the flow.