This work describes the thermoresponsive transition in polystyrene-block-poly(N-isopropylacrylamide)-block-polystyrene (PS-block-PNIPAM-block-PS) triblock copolymer hydrogels, as observed by both direct and reciprocal space in-situ characterization. The hydrogel morphology was studied in both the dry and wet state, at temperatures below and beyond the coil-globule transition of PNIPAM, using vitrified ice cryotransmission electron microscopy (cryo-TEM), in-situ freeze-drying technique, and small-angle X-ray scattering (SAXS). The selected PS-block-PNIPAM-block-PS triblock copolymers were intentionally designed in such a molecular architecture to self-assemble into spherical and bicontinuous morphology with the poly(N-isopropylacrylamide) forming the continuous matrix. The phase behavior in bulk was directly investigated by SAXS as a function of temperature, while free-standing polymer thin films of samples quenched from different temperatures, allowed observing by cryo-TEM the changes in hydrogel microstructure. Finally, sublimation of water via controlled freeze-drying in the TEM column allowed studying systems without the presence of vitrified water, which enables direct imaging of the densely connected physically cross-linked polymer network. By combining these techniques on samples exhibiting both spherical and gyroidal morphologies, it was demonstrated that (i) PNIPAM form physically connected networks in spherical structures and bicontinuous morphologies in the gyroidal phase, (ii) in PNIPAM chains strands are strongly stretched above the polymer coil-to-globule transition, and (iii) Surprisingly, upon the gel swelling process, the PS domains undergo extensive plastic deformation although temperature is always maintained well below the PS glass transition bulk temperature. The possible physical mechanisms responsible for this plastic deformation can be understood in terms of the dependence of PS glass transition temperature on the size of nanometer-scaled domains.