Work-family conflict constitutes an important source of occupational stress predicting teachers' burnout, and cognitive variables have shown to be core structures in explaining human adaptation to stress. Nevertheless, the role of cognitive appraisal needs to be fully analysed to comprehend how it can mediate the relationship between stress and burnout. In order to understand the potential mediation of cognitive appraisal in the relationship between stress and burnout, we adopted conceptual models of stress that highlighted the value of cognitive appraisal on positive and negative reactions to work demands. Also, we analysed the potential moderation of sex and age in the relationship between work-family conflict, cognitive appraisal, and burnout due to inconsistent findings on how these personal variables can interfere on these relations. In this study, we used structural equation modelling (SEM) to test the mediating of cognitive appraisal in the relationship between work-family conflicts and burnout. A survey with measures of work-family conflicts, cognitive appraisal, and burnout was administered to the participants consisting of 438 Portuguese teachers from kindergarten through high school, aged between 28 and 67 years (M = 46.85; SD = 7.88), 304 of whom were females (69.41%). The results confirmed that cognitive appraisal partially mediated the relationship between work-family conflict and burnout. The mediation effect of cognitive appraisal on the relationship between work-family conflict and burnout was invariant regardless of teachers' sex or age. In sum, cognitive appraisal should be considered in order to understand teachers' adaptation to work.