Self-assembling properties of poly(sodium acrylate) grafted with dodecyl [C12], PAAgC12, or poly(N-isopropylacrylamide) [PNIPA] side chains, PAAgPNIPA, were studied in unentangled semidilute aqueous solution. While PAAgC12 self-associates through hydrophobic interactions, the gelation of PAAgPNIPA is triggered by heating in response to the lower critical solution temperature of PNIPA (LCST similar to 32 degrees C). The local structure of the physical networks was investigated by small-angle neutron scattering, and the scattering patterns were described using a polydisperse sphere model taking into account hard-sphere interactions. This model allow us to draw a realistic picture of physical gels with quantitative information concerning the size of hydrophobic cores, the volume fraction of stickers in the aggregates, the fraction of stickers which take part in the aggregation process, the range of repulsive interactions, and the structural modifications induced by temperature. The description of the network is in good agreement with complementary data obtained from DSC and C-13 NMR. In the present work, a special emphasis has been given to the important relationship existing between the viscoelastic properties of associating polymer solutions and the binding energy of stickers leaving temporarily the micellar junction. Depending on the endothermic or exothermic nature of the disengagement process of the sticker (heat of demicellization), the relaxation time of the network and the viscoelastic properties will either decrease or increase with the temperature. The consequence is that aqueous solutions of PAAgC12 and PAAgPNIPA exhibit opposite rheological properties with the temperature, namely thermothinning and thermothickening. By mixing these two copolymers, we show that intermediate properties can be obtained but in that case a microphase-separated network is obtained as a result of copolymer segregation.