Oscillatory shear rheometry is used to study the mechanical response of single-walled carbon nanotubes dispersed in solutions of acrylic diblock or triblock copolymers in 2-ethyl-1-hexanol. Thermal transitions in the copolymer solutions provide a route for the easy processing of these composite materials, with excellent dispersion of the nanotubes as verified by near-infrared photoluminescence spectroscopy. The nanotube dispersions form elastic networks with proper-ties that are controlled by the junction points between nanotubes, featuring a temperature-dependent elastic response that is controlled by the dynamic properties of the matrix copolymer solution. The data are consistent with the formation of micelle-like aggregates around the nanotubes. At low temperatures the core-forming poly(methyl methacrylate) blocks are glassy, and the overall mechanical response of the composite does not evolve with time. At higher temperatures the enhanced mobility of the core-forming blocks enables the junctions to achieve more intimate nanotube-nanotube contact, and the composite modulus increases with time. These aging effects are observed in both diblock and triblock copolymer solutions but are partially reversed in the triblock solutions by cooling through the gel transition of the triblock copolymer. This result is attributed to the generation of internal stresses during gelation and the ability of these stresses to break or weaken the nanotube junctions.