Questions of temporality are at the heart of climate change discourse: Does one think of climate change primarily as an event happening in the present, or as something that will take place in the future? By when must we take action to prevent its worst consequences? This article presents the first large-scale assessment of the structure and evolution of temporalities expressed in U.S. media discussions on climate change (2000 to 2021). To do so, we developed a novel computational framework for detecting and interpreting temporal expressions in textual data. Our analyses yield three main findings: First, temporal horizons for climate change have continuously shrunk since 2000, stably targeting, on average, the year 2060. However, second, while anticipated effects are getting closer, horizons for the coordination of climate action have remained highly stable, averaging around 16 years into the future at any given time. Third, contrasting the stability of explicitly stated horizons, we find a sharply expanding discourse of urgency patterned by outbursts of urgency: sudden surges in calls for immediate action or warnings against climate change’s devastating consequences during events like the 2020 California wildfires. By uncovering this disjuncture of different forms of temporality, we illuminate a crucial aspect of the climate change debate, contribute to the sociological theory of events, and identify some of the conditions underlying climate inaction.