The extent and nature of thermal fluctuations in the innovative class of cross-linked polymers called cyclodextrin nanosponges (CDNS) are investigated, on the picosecond time scale, through elastic and quasielastic neutron scattering experiments. Nanosponges are complex 3D polymer networks where covalent bonds connecting different cyclodextrin (CD) units and intra- and inter-molecular hydrogen-bond interactions cooperate to define the molecular architecture and fast dynamics of the polymer. The study presented here aims to clarify the nature of the conformational rearrangements activated by increasing temperature in the nanosponge polymer, and the constraints imposed by intra- and inter-molecular hydrogen-bond patterns on the internal dynamics of the macromolecule. The results suggest a picture, in which conformational rearrangements involving the torsion of the OH groups around the C–O bonds dominate the internal dynamics of the polymer over the picosecond time scale. Moreover, the estimated values of mean square displacements reveal that the motions of the hydrogen atoms in the nanosponges are progressively hampered as the cross-linking degree of the polymer is increased. Finally, the study of the molecular relaxations suggests a dynamical rearrangement of the hydrogen-bond networks, which is characterized by a jump diffusion motion of the more mobile hydrogen atoms belonging to the OH groups of the CD units. All these findings add further contribution to the rational comprehensive view of the dynamics of these macromolecules, which may be particularly beneficial in designing new drug-delivery systems with tuneable inclusion/release properties.