Aqueous solutions of a double responsive P2VP₆₂-b-PEO₄₅₂-b-P(GME₃₆-co-EGE₃₆) triblock terpolymer were investigated by means of small-angle neutron scattering (SANS) in order to derive information about structural changes going along with the temperature triggered gel-sol-gel transition at pH = 7, and the sol-gel transition at pH = 3.5, respectively, observed by rheology. SANS measurements on dilute samples at different pH and temperature confirmed the formation of core-shell-corona micelles under conditions, where only one of the outer blocks is insoluble. In addition, temperature-dependent scattering experiments were performed for higher volume fractions, that is, the concentration range where hydrogels were formed. This allowed us to identify the structural transitions, being responsible for the gel-sol-gel transition at pH = 7, and the structure of the gel phase formed at low pH and elevated temperatures.