Core-shell microgels made of the thermoresponsive polymer poly(N-isopropylacrylamide) (PNIPAM) and silica nanoparticles as inorganic cores were investigated by dynamic light scattering (DLS) and small angle neutron scattering (SANS). In order to study the response of the particles upon changes of temperature, experiments were done in a temperature interval close to the volume phase transition temperature of the PNIPAM shell. While DLS probes the hydrodynamic dimensions of the particles, determining their centre of mass diffusion, SANS provides the correlation length ξ of the PNIPAM network. Additionally, the composite particles were characterised by electron microscopy as well as atomic force microscopy to reveal the core-shell structure and at the same time the approximate dimensions and the shape of the microgels.