Digital twin systems can benefit from the integration of artificial intelligence (AI) algorithms for providing for example some predictive capabilities or supporting internal decision-making. As AI algorithms are often opaque, it becomes necessary to explain their decisions to a human operator working with the digital twin. In this study, we investigate the integration of explainable AI techniques with digital twins, which we termed XAI-DT system. We define the concept of XAI-DT system and provide a use case in smart buildings, where explainable AI is used to forecast CO₂ concentration. Further, we present a core architectural model for our digital twin, outlining its interaction with the smart building and its internal processing. We evaluate five AI algorithms and compare their explainability for the operator and the entire digital twin model based on standard explainability properties from the literature.