Extreme events, such as heat waves, are predicted to increase in frequency, duration, and severity as a consequence of climate change. However, global change research generally focuses on increases in mean temperatures and fails to address the potential impacts of increasingly severe heat waves. In addition, climate change may interact with another primary threat to biodiversity, non‐native species invasions. We assessed the impacts of a short‐term heat wave on the marine epibenthic fouling community of Bodega Harbor, California, USA, by exposing experimental mesocosms to a simulated heat wave in the laboratory and then monitoring community development in the field. We hypothesized that (1) juveniles would be more susceptible to heat waves than adults, (2) native species would be more susceptible than non‐native species, and (3) non‐native species would recover more quickly than native species. We observed no effect of the heat wave on juvenile species richness, either initially or during the recovery period, relative to communities at ambient seawater temperatures. In contrast, total adult species richness initially declined in response to the heat wave. Adult community composition also changed in heat‐wave treatments, with non‐natives representing the majority of species and occupying more cover than native species. The reduction in native richness associated with the heat wave persisted through the recovery period, whereas invasive richness was actually higher on heat‐wave versus ambient plates at 95 days. Heat waves have the potential to alter the composition of this community because of species‐, taxon‐, and/or origin‐specific responses; for example, non‐native bryozoans displayed greater resistance than native and non‐native tunicates. Recovery from the heat wave occurred via growth of resistant individuals and larval recruitment. Our study highlights the importance of considering species' and community responses to heat waves, and not just mean predicted temperature increases, to evaluate the consequences of climate change.