A disruptive digitalization recently occurred that led to the fast adoption of virtual teams. However, membership diversity and team virtuality threaten members’ well-being, especially if faultlines appear (i.e., subgroups). Considering the job demands–resources model and the role of group affect in shaping members’ perceptions of well-being, we test the effectiveness of a short-term affect management training for increasing members’ eudaimonic well-being. Moreover, based on the trait activation theory and the contingent configuration approach, we draw on the personality composition literature to test how different openness to experience configurations of team level and diversity together moderate the effect of the training. Hypotheses were tested using a pre–post design in an online randomized controlled trial in an educational context in Spain, with a sample of 52 virtual teams with faultlines. Results show that affect management training increased eudaimonic well-being. Furthermore, there was a moderation effect (three-way interaction) of openness to experience configurations, so that the training was more effective in teams with high levels and low diversity in openness to experience. We discuss implications for training, well-being, and personality composition literature. This study helps organizations develop sustainable virtual teams with engaged members through affect management training and selection processes based on the openness to experience trait.