Predicting the impacts of climate change requires knowledge of the potential to adapt to rising temperatures, which is unknown for most species. Adaptive potential may be especially important in tropical species that have narrow thermal ranges and live close to their thermal optimum. We used the animal model to estimate heritability, genotype by environment interactions and nongenetic maternal components of phenotypic variation in fitness-related traits in the coral reef damselfish, Acanthochromis polyacanthus. Offspring of wild-caught breeding pairs were reared for two generations at current-day and two elevated temperature treatments (+1.5 and +3.0 °C) consistent with climate change projections. Length, weight, body condition and metabolic traits (resting and maximum metabolic rate and net aerobic scope) were measured at four stages of juvenile development. Additive genetic variation was low for length and weight at 0 and 15 days posthatching (dph), but increased significantly at 30 dph. By contrast, nongenetic maternal effects on length, weight and body condition were high at 0 and 15 dph and became weaker at 30 dph. Metabolic traits, including net aerobic scope, exhibited high heritability at 90 dph. Furthermore, significant genotype x environment interactions indicated potential for adaptation of maximum metabolic rate and net aerobic scope at higher temperatures. Net aerobic scope was negatively correlated with weight, indicating that any adaptation of metabolic traits at higher temperatures could be accompanied by a reduction in body size. Finally, estimated breeding values for metabolic traits in F2 offspring were significantly affected by the parental rearing environment. Breeding values at higher temperatures were highest for transgenerationally acclimated fish, suggesting a possible role for epigenetic mechanisms in adaptive responses of metabolic traits. These results indicate a high potential for adaptation of aerobic scope to higher temperatures, which could enable reef fish populations to maintain their performance as ocean temperatures rise.