The properties of the complexes formed in water between the cationic surfactant dodecyltrimethylammonium bromide (DTAB) and the comb-type anionic polyelectrolyte poly(sodium acrylate-co-sodium 2-acrylamido-2-methylpropanesulfonate)-g-poly(N-isopropylacrylamide) (P(NaA-co-NaAMPS)-g-PNIPAM) were investigated in dilute aqueous solutions and compared to the properties of the complexes formed between DTAB and poly(sodium acrylate-co-sodium 2-acrylamido-2-methylpropanesulfonate)-g-poly(N,N-dimethylaerylamide) (P(NaA-co-NaAMPS)-g-PDMAM). It was found that, contrary to the water-insoluble complexes formed between the linear polyelectrolyte P(NaA-co-NaAMPS) and the oppositely charged DTAB, the complexes formed between DTAB and the comb-type copolymers, either P(NaA-co-NaAMPS)-g-PNIPAM or P(NaA-co-NaAMPS)-g-PDMAM, maintain water solubility at room temperature. In both cases, complexation is accompanied by charge neutralization, formation of hydrophobic microdomains, and a substantial decrease of the reduced viscosity of the aqueous solution. Contrary to the P(NaA-co-NaAMPS)-g-PDMAM/DTAB complexes, the P(NaA-co-NaAMPS)-g-PNIPAM/DTAB complexes separate out from water upon heating, due to the lower critical solution temperature behavior of the PNIPAM side chains. At high DTAB concentrations, mixed aggregates between the PNIPAM side chains and DTAB cations are formed, leading to the indirect introduction of positive charges in the complex and to the elevation of the phase separation temperature.