In this work, we study temperature-induced state change of an aqueous solution of triblock copolymer composed of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide), PEO-PPO-PEO (Pluronic F127), at different concentrations using rheology. While this temperature-dependent state change visually appears like a liquid-soft solid transition, and the soft solid state has been termed as a gel in the literature, there is a debate regarding the precise microstructure of the soft solid state. We observe that over a concentration domain of interest, an aqueous solution of F127 overwhelmingly demonstrates all the characteristic rheological features of not just a sol-gel-glass transition at low temperatures and glass-liquid transition at high temperatures, but also that associated with the individual states, such as sol, post-gel, and glass. The temperature at which the gel-glass transition is observed decreases while the temperature associated with glass-liquid transition increases with an increase in the concentration of F127. Based on the observed behavior, we propose a mechanism that considers the change in micelle volume fraction and alteration of the hydrophilicity of PEO corona as a function of temperature. Finally, we construct a phase diagram and discuss the similarities and differences with respect to various phase diagrams of F127 solution available in the literature. Published under an exclusive license by AIP Publishing.