Graft copolymers of poly(2-vinylpyridine), P2VP, grafted to a backbone of poly(N-isopropyl acrylamide), PNIPAM, are investigated concerning their thermosensitive behavior in aqueous solution. H-1 NMR monitors the coil-to-globule transition by quantifying the fraction of mobile segments in the liquid state. Field gradient NMR diffusion studies reveal a decrease of the hydrodynamic radius with temperature as the lower critical solution temperature (LCST) is approached. The LCST and the width of the transition of PNIPAM are increasing with grafting density and decreasing upon salt addition, which is attributed to electrostatic forces. The grafted segments become partially immobilized only for low grafting density. For high grafting density a fraction of the backbone segments remains mobile even above the LCST. H-2 spin relaxation rates of the hydration water indicate the presence of water molecules with very slow dynamics in the transition regime, whereas above and below the transition only fast water dynamics is found.