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Population growth metrics such as R-0 are usually asymmetric functions of temperature, with cold-skewed curves arising when the positive effects of a temperature increase outweigh the negative effects, and warm-skewed curves arising in the opposite case. Classically, cold-skewed curves are interpreted as more beneficial to a species under climate warming, because cold-skewness implies increased population growth over a larger proportion of the species's fundamental thermal niche than warm-skewness. However, inference based on the shape of the fitness curve alone, and without considering the synergistic effects of net reproduction, density and dispersal, may yield an incomplete understanding of climate change impacts. We formulate a moving-habitat integrodifference equation model to evaluate how 'fitness curve skewness affects species' range size and abundance during climate warming. In contrast to classic interpretations, we find that climate 'arming adversely affects populations with cold-skewed fitness curves, positively affects populations with warm-skewed curves and has relatively little or mixed effects on populations with symmetric curves. Our results highlight the synergistic effects of fitness curve skewness, spatially hetero, geneous densities and dispersal in climate change impact analyses, and that the common approach of mapping changes only in R-0 may be misleading.