Synthetic polycations have shown promise as gene delivery vehicles but suffer from an unacceptable toxicity and low transfection efficiency. Novel architectures are being explored to increase transfection efficiency, including copolymers with a thermoresponsive character. The physicochemical characterization of a family of copolymers comprising a core of the cationic polymer poly(ethylene imine) (PEI) with differing thermoresponsive poly( N-isopropylacrylamide) (PNIPAM) grafts has been carried out using pulsed-gradient spin-echo NMR (PGSE-NMR) and small-angle neutron scattering (SANS). For the copolymers that have longer chain PNIPAM grafts, there is clear evidence of the collapse of the grafts with increasing temperature and the associated emergence of an attractive interpolymer interaction. These facets depend on the number of PNIPAM grafts attached to the PEI core. While a collapse in the smaller PNIPAM grafts is observed for the third polymer, there is no appearance of the interpolymer attractive interaction. These observations provide further insight into the association behavior of these copolymers, which is fundamental to developing a full understanding of how they interact with nucleic acids. Furthermore, the differing behaviors of the three copolymers over temperatures in which the PNIPAM blocks undergo coil-to-globule transitions is indicative of changes in the presentation of charged-core and hydrophobic chain components, which are key factors affecting nucleic acid binding and, ultimately, cell transfection ability.