Opinion dynamics models describe the evolution of behavioral changes within social networks and are essential for informing strategies aimed at fostering positive collective changes, such as climate action initiatives. When applied to social media interactions, these models typically represent social exchanges in a dyadic format to allow for a convenient encoding of interactions into a graph where edges represent the flow of information from one individual to another. However, this structural assumption fails to adequately reflect the nature of group discussions prevalent on many social media platforms. To address this limitation, we present a temporal hypergraph model that effectively captures the group dynamics inherent in conversational threads, and we apply it to discussions about climate change on Reddit. This model predicts temporal shifts in stance towards climate issues at the level of individual users. In contrast to traditional studies in opinion dynamics that typically rely on simulations or limited empirical validation, our approach is tested against a comprehensive ground truth estimated by a large language model at the level of individual user comments. Our findings demonstrate that using hypergraphs to model group interactions yields superior predictions of the microscopic dynamics of opinion formation, compared to state-of-the-art models based on dyadic interactions. Although our research contributes to the understanding of these complex social systems, significant challenges remain in capturing the nuances of how opinions are formed and evolve within online spaces.