Aqueous solutions of a thermoresponsive amphiphilic diblock copolymer, containing poly(N-isopropylacrylamide), in the presence of the anionic sodium dodecyl sulfate (SDS) surfactant can undergo a temperature-induced transition from loose intermicellar clusters to collapsed core-shell nanostructures. The polymer-surfactant mixtures have been characterized with the aid of turbidity, small-angle neutron scattering (SANS), intensity light scattering (ILS), dynamic light scattering (DLS), shear viscosity, and rheo-small angle light scattering (rheo-SALS). In the absence of SDS, compressed intermicellar structures are formed at intermediate temperatures, and at higher temperatures further aggregation is detected. The SANS results disclose a structure peak in the scattered intensity profile at the highest measured temperature. This peak is ascribed to the formation of ordered structures (crystallites). In the presence of a low amount of SDS, a strong collapse of the intermicellar clusters is observed at moderate temperatures, and only a slight renewed interpolymer association is found at higher temperatures because of repulsive electrostatic interactions. Finally, at moderate surfactant concentrations, temperature-induced loose intermicellar clusters are detected but no shrinking was registered in the considered temperature range. At a high level of SDS addition, large polymer-surfactant complexes appear at low temperatures, and these species are compressed at elevated temperatures. The rheo-SALS results show that the transition structures are rather fragile under the influence of shear flow.