Demand response can be an effective means for power system operators to compensate fluctuating renewable generation, to avoid grid congestion, and to cope with other contingencies. Buildings equipped with electric heating systems can provide demand-response services because their electricity consumption is inherently flexible due to their thermal inertia. This paper reports on the results of a large-scale demand-response demonstration involving a population of more than 300 residential buildings with heat pumps. Based on a procedure to autonomously estimate the electric flexibility of individual systems from energy meter data and outdoor air temperature measurements, we show how the aggregate demand-response potential of the systems can be quantified and predicted. The results of various experiments illustrate that load reductions of 40-65% of the total load can be achieved by throttling the heat pumps, and that these load reductions can be delivered precisely with a median absolute percentage error of below 7%. In addition, a rebound damping strategy is proposed that was shown to reduce the peak rebound power by 50% in practice.