There are numerous and miscellaneous sources of online information. Judging whether it is a rumor in a timely and accurate manner is a crucial issue in the research of the cognitive domain of social media. Most of the previous studies have mainly concentrated on the text content of rumors, user characteristics, or the inherent features confined to the propagation mode, ignoring the key clues of the collective emotions generated by users’ participation in event discussions and the emotional steady-state characteristics hidden in the spread of rumors. In this study, a social network rumor detection method that is oriented by collective emotional stabilization and integrates temporal and spatial steady-state features is proposed. Based on the text features and user behaviors in rumor propagation, the temporal and spatial relationship steady-state features of collective emotions are combined for the first time, which can achieve strong expressiveness and detection accuracy. Specifically, this method takes the emotional keywords of users’ attitude towards a certain event or topic as the basis and uses recurrent neural networks to construct emotional steady-state features of the temporal relationship, enabling the collective emotions to have temporally consistent features with strong expressiveness, which can reflect the convergence effect of the collective emotions over time. The heterogeneous graph neural network is utilized to establish the connections between users and keywords, as well as between texts and keywords so that the collective emotions possess the fine-grained collective emotional steady-state features of the spatial relationship. Finally, the two types of local steady-state features are fused, possessing globality and improving the feature expression. Further classification can obtain the rumor detection results. The proposed method is run on two internationally publicly available and widely used Twitter datasets. Compared with the best-performing method in the baselines, the accuracy is improved by 3.4% and 3.2% respectively; the T-F1 value is improved by 3.0% and 1.8% respectively; the N-F1 value is improved by 2.7% and 2.3% respectively; the U-F1 value is improved by 2.3% and 1.0% respectively.