A small amount of alumina nanoparticles in polymethylmethacrylate causes a sharp depression of the glass transition temperature (Tg) accompanied by a toughening of the composite. We investigated this phenomenon using multispeckle x-ray photon correlation spectroscopy. Measurements reveal a dynamic structure factor that has the form exp[-(t/taua)beta], with beta greater than 1. We show for the first time that beta(T) tracks the internal stress at the polymer-particle interface. The internal stress, which we propose arises due to the entropic penalty that the polymer faces in the presence of the nanoparticles, engenders temporally heterogeneous dynamics. In the jammed glassy state, we show that the dominant fast relaxation mode--taumax--aided by a weak dewetting interface relieves the stress and follows the variations in Tg.