An investigation of the volume transition in colloidal core-shell particles composed of a temperature-independent polystyrene core and a shell of thermosensitive cross-linked polymer chains by small-angle X-ray scattering (SAXS) is presented. The PS cores of the particles have a diameter of 80 nm whereas the shell composed of cross-linked poly(N-isopropylacrylamide) has a thickness of 32 nm in the swollen state at 25 degrees C and of 18 nm after shrinking by a continuous volume transition. The SAXS intensities measured at high scattering angles could be described by a Lorentz-type function at both states. This indicates the presence of liquidlike local concentration fluctuations of the gel which are still present in the shrunken state. The correlation lengths xi measured in both states are of the order of a few nanometers (25 degrees C, xi = 3.2 nm; 50 degrees C, xi = 2.1 nm). The present analysis therefore shows that the core-shell microgels behave in a distinctively different manner than ordinary thermosensitive gels: The cross-linked chains in the shell are bound to a solid boundary independent of temperature. The spatial constraint by this boundary decreases the maximum degree of swelling but also prevents a full collapse of the network above the volume transition.