Model Predictive Control for room temperature control in buildings is an effective approach to energy management in buildings. However, the development and maintenance of physical models may be a bottleneck for widespread real life application, especially for residential buildings. Data Predictive Control is an attempt to address this problem by learning the behaviour of the building from historical data and thus reducing the modelling effort. Here, we present an application of a Data Predictive Control approach, based on Random Forests with affine functions and convex optimization, to control the room temperature in a real life apartment. When compared to a conventional hysteresis controller, the applied approach saves 24.9% of cooling energy while reducing the integral of comfort constraint violations by 72.0% in a six-day experiment. A second experiment shows limitations when longer prediction horizons are needed. They are discussed together with directions of future work.