Energy projects aimed at a sustainable energy transition can trigger strong negative emotions and resistance from the public. While practitioners are increasingly realising that they cannot simply ignore public emotions, they struggle with how to deal with people's emotional responses and how to secure public acceptability of sustainable energy projects. We argue that a first critical step in order to adequately address emotional responses to energy projects is to understand where these emotional responses come from. We introduce a value-based approach, which entails that different characteristics of energy projects may violate or support people's core values, which evokes emotions in people. We present a theoretical framework of the relationship between people's values, the (perceived) implications of energy projects for these values, and people's emotional responses to energy projects. We give examples from case studies in the literature to substantiate our reasoning, and we offer directions for future research. Our novel approach provides critical insights for project developers, decision makers, engineers, and scientists who aim to better understand the human dimension of a sustainable energy transition.