Well-dispersed, solvent-free silica nanoparticles tethered with polymers exhibit soft glassy rheology and jamming behavior because of the cages induced by interpenetrated chains. In this study, we use small-angle X-ray scattering and rheology to investigate slow structural and mechanical evolution of a soft glassy material composed of silica nanoparticles densely grafted with poly(ethylene glycol) methyl ether (mPEG) chains. We observe a significant equilibration process that has not been reported previously and show that the process is thermally activated and associated with local rearrangements of tethered chains to their equilibrium conformations. At a fixed temperature, the strength of the equilibrated cages increases significantly, relative to their unequilibrated values, but decreases in a predictable manner as the temperature rises. A simple geometrical model is used to rationalize these observations in terms of corona interpenetration, cage dynamics, and yielding of self-suspended nanoparticles.