Highly-branched poly(N-isopropyl acrylamide)s in water pass through coil-to-globule transitions. Using calorimetry and the colour change of a solvatochromic dye within the polymer, we show that some compositions have biphasic core–shell morphologies, with globular cores and open coil shells. The two-phase structure is favoured by increased branching and arises because the chain ends penetrate only to a limited degree into the polymer coil.