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Focusing on the air-conditioner, this paper considers the real-time model learning and the adaptation algorithm to the indoor environment, simultaneously. It is clarified that the Constant-Trace Algorithm is effective for the adaptation, which consists of the detection of disturbances (external factors to change the amount of heat in the room) and the switching between the model learning with and without the disturbances. Also, this paper estimates the perturbation of the amount of heat based on the disturbance detection. In addition, this paper validates the effectiveness of our method by experiments.