In order to evaluate side-effect of power limitation due to the Fast Automated Demand Response (FastADR) for building air-conditioning facilities, a prediction model on short time change of average room temperature has been developed. A room temperature indexis defined as a weighted average of the entire building for room temperature deviations from the setpoints. The index is assumed to be used to divide total FastADRrequest to distribute power limitation commands to each building.In order to predict five-minute-change of the index, our combined mathematical model of an auto regression (AR) and a neural network (NN) is proposed.In the experimental results, the combined model showedthe root mean square error (RMSE) of 0.23 degrees, in comparison with 0.37 and 0.26 for conventional single NN and AR models, respectively. This result is satisfactory prediction for required comfort of approximately 1 degree Celsius allowance.