ObjectivesThe United Nations recognize the importance of balancing the needs of people and the planetary systems on which human health relies. This paper investigates the role that climate change has on human health via its influence on climate anxiety.DesignWe conducted an intensive longitudinal study.MethodsParticipants reported levels of climate anxiety, generalized anxiety and an array of health behaviours at 20 consecutive time points, 2 weeks apart.ResultsA network analysis shows climate anxiety and generalized anxiety not to covary, and higher levels of climate anxiety not to covary with health behaviours, except for higher levels of alcohol consumption at the within‐participant level. Generalized anxiety showed completely distinct patterns of covariation with health behaviours compared with climate anxiety.ConclusionsOur findings imply that climate anxiety, as conceptualized and measured in the current study, is not in itself functionally impairing in terms of associations with unhealthy behaviours, and is distinct from generalized anxiety. The results also imply that interventions to induce anxiety about the climate might not always have significant impacts on health and well‐being.