Elastomers filled with hard nanoparticles are of great technical importance for the rubber industry. In general, fillers improve mechanical properties of polymer materials, e.g. elastic moduli, tensile strength etc. The smaller the size of the particles, the larger is the interface where interactions between polymer molecules and fillers can generate new properties. Using temperature-modulated differential scanning calorimetry and dynamic mechanical analysis, we investigated the properties of pure styrene-butadiene rubber (SBR) and SBR/alumina nanoparticles. Beside a reinforcement effect seen in the complex elastic moduli, small amounts of nanoparticles of about 2 wt% interestingly lead to an acceleration of the relaxation modes responsible for the thermal glass transition. This leads to a minimum in the glass transition temperature as a function of nanoparticle content in the vicinity of this critical concentration. The frequency dependent elastic moduli are used to discuss the possible reduction of the entanglement of rubber molecules as one cause for this unexpected behavior.