We have investigated the formation of vesicles in the binary system of a triblock copolymer of poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO) with the average composition EO5PO68EO5 in water. Vesicles are formed when a solution of unimers is heated into a two-phase region where, at equilibrium, a concentrated lamellar phase coexists with a dilute solution of unimers. The vesicles were characterized by cryo-TEM, static and dynamic light scattering, and NMR experiments. The average vesicle radius is approximately 60 nm, with an exponential size distribution, and the concentration of vesicles depends strongly on the temperature. The vesicles remain stationary on the time scale of hours. A striking observation is that, on this time scale, both the vesicle size distribution and the concentration of vesicles are reversible with respect to temperature cycles. However, on the time scale of weeks a sedimentation is observed in the solutions.