The nature of local atomic and electronic structure at the nanoscale is of both fundamental and technological importance. For example, supported metal nanoclusters exhibit a number of unusual phenomena including large structural disorder and bond-length contraction with increasing temperature. We investigate this behavior for a prototypical ten atom Pt cluster supported on $\ensuremath{\gamma}$ alumina using temperature-dependent, real-time simulations based on density functional theory/molecular-dynamics and x-ray spectroscopy theory. The simulations reveal a complex dynamical structure on multiple-time scales including librational motion of the center of mass and fluctuating bonding characteristics, which explain many of the unusual properties.