Control systems are essential to support the use of building structures as short-term thermal energy storage (TES). Due to modeling and forecast imperfections, the controller must be able to deal with uncertainties. This paper proposes a robust model predictive controller (MPC) with a new uncertainty set construction technique to regulate the heat supply in a building envelope. We extend the Support Vector Clustering-based set construction technique to estimate modeling and forecast uncertainty sets. Subsequently, we integrate the sets into a Min-Max MPC framework to ensure robust feasibility by tightening the constraints. The resulting controller successfully deals with modeling and forecast uncertainties. The quality of the presented framework is compared with a nominal MPC and a robust MPC with different uncertainty set estimates. On the basis of a numerical simulation, we demonstrate that the proposed controller successfully maintains the room temperature within the comfort limits. The result also shows that our MPC is less conservative than the controller designed using a box-shaped non-falsified parametric uncertainty set.