Poly(N-isopropylacrylamide)-block-poly(acrylic acid), PNIPAAm-b-PAA, with low polydispersity was prepared by reversible addition-fragmentation chain transfer (RAFT) polymerization in methanol. The block copolymers respond to both temperature and pH stimuli. The behaviour of the double-responsive block copolymers in solution was investigated by dynamic light scattering, temperature-sweep NMR, cryogenic transmission electron microscopy, and IR spectroscopy. The block copolymers form micelles in aqueous solutions in dependence of pH and temperature. Cloud point measurements indicated the formation of larger aggregates at pH 4.5 and temperatures above the lower critical solution temperature (LCST) of PNIPAAm. The solution behaviour is strongly influenced by hydrogen bonding interactions between the NIPAAm and acrylic acid blocks.