Amphiphilic diblock copolymers composed of a polymeric ionic liquid, PIL, and poly(N-isopropylacrylamide), PNIPAM, have been synthesized using RAFT reactions. The length of the PIL block was kept constant while the molecular mass of the PNIPAM block was varied. The PIL was poly(2-(1-butylimidazolium-3-yl) ethyl methacrylate tetrafluoroborate) which is insoluble in water owing to the bulky hydrophobic counterion. When the PNIPAM block was long enough, the polymers formed spherical micelles in water, which showed thermally responsive behaviour. Colloidally stable particles could be prepared also from the homopolymeric PIL. PNIPAM affects noticeably the properties of the PIL, and also the polycation has a strong effect on the thermal properties of PNIPAM in aqueous dispersions. As a reference, a polymer where bromide was the counter ion instead of the tetrafluoroborate ion was synthesized, providing a water soluble PIL block. The core-shell micelles formed by amphiphilic block copolymers in pure water and those by double-hydrophilic polymers in aqueous NaBF4 undergo partial structural inversion upon the thermal collapse of PNIPAM.