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Understanding the processes that influence range expansions during climate warming is paramount for predicting population extirpations and preparing for the arrival of non-native species. While climate warming occurs over a background of variation due to cyclical processes and irregular events, the temporal structure of the thermal environment is largely ignored when forecasting the dynamics of non-native species. Ecological theory predicts that high levels of temporal autocorrelation in the environment– relatedness between conditions occurring in close temporal proximity– will favor populations that would otherwise have an average negative growth rate by increasing the duration of favorable environmental periods. Here, we invoke such theory to explain the success of biological invasions and evaluate the hypothesis that sustained periods of high environmental temperature can act synergistically with increases in mean temperature to favor the establishment of non-native species. We conduct a 60-day field mesocosm experiment to measure the population dynamics of the non-native cladoceran zooplankter Daphnia lumholtzi and a native congener Daphnia pulex in ambient temperature environments (control), warmed with recurrent periods of high environmental temperatures (uncorrelated-warmed), or warmed with sustained periods of high environmental temperatures (autocorrelated-warmed), such that both warmed treatments exhibited the same mean temperature but exhibited different temporal structures of their thermal environments. Maximum D. lumholtzi densities in the warmed-autocorrelated treatment were three- and eight-fold higher relative to warmed-uncorrelated and control treatments, respectively. Yet, D. lumholtzi performed poorly across all experimental treatment relative to D. pulex and were undetectable the end of the experiment. Using mathematical models we show that this increase in performance can occur alongside increasing temporal autocorrelation, and should occur over a broad range of warming scenarios. These results provide both empirical and theoretical evidence that the temporal structure of the environment can influence the performance of species undergoing range expansions due to climate warming. This article is protected by copyright. All rights reserved.