How the ability to acclimate will impact individual performance and ecological interactions under climate change remains poorly understood. Theory predicts that the benefit an organism can gain from acclimating depends on the rate at which temperatures change relative to the time it takes to induce beneficial acclimation. Here, we present a conceptual model showing how slower seasonal changes under climate change can alter species' relative performance when they differ in acclimation rate and magnitude. To test predictions from theory, we performed a microcosm experiment where we reared a mid- and a high-latitude damselfly species alone or together under the rapid seasonality currently experienced at 62 degrees N and the slower seasonality predicted for this latitude under climate change and measured larval growth and survival. To separate acclimation effects from fixed thermal responses, we simulated growth trajectories based on species' growth rates at constant temperatures and quantified how much and how fast species needed to acclimate to match the observed growth trajectories. Consistent with our predictions, the results showed that the midlatitude species had a greater capacity for acclimation than the high-latitude species. Furthermore, since acclimation occurred at a slower rate than seasonal temperature changes, the midlatitude species had a small growth advantage over the high-latitude species under the current seasonality but a greater growth advantage under the slower seasonality predicted for this latitude under climate change. In addition, the two species did not differ in survival under the current seasonality, but the midlatitude species had higher survival under the predicted climate change scenario, possibly because rates of cannibalism were lower when smaller heterospecifics were present. These findings highlight the need to incorporate acclimation rates in ecological models.