Ecological modeling shows that even small, gradual changes in body size in a fish population can have large effects on natural mortality, biomass, and catch. However, efforts to model the impact of climate change on fish growth have been hampered by a lack of long-term (multidecadal) data needed to understand the effects of temperature on growth rates in natural environments. We used a combination of dendrochronology techniques and additive mixed-effects modeling to examine the sensitivity of growth in a long-lived (up to 70 years), endemic marine fish, the western blue groper (Achoerodus gouldii), to changes in water temperature. A multi-decadal biochronology (1952–2003) of growth was constructed from the otoliths of 56 fish collected off the southwestern coast of Western Australia, and we tested for correlations between the mean index chronology and a range of potential environmental drivers. The chronology was significantly correlated with sea surface temperature in the region, but common variance among individuals was low. This suggests that this species has been relatively insensitive to past variations in climate. Growth increment and age data were also used in an additive mixed model to predict otolith growth and body size later this century. Although growth was relatively insensitive to changes in temperature, the model results suggested that a fish aged 20 in 2099 would have an otolith about 10% larger and a body size about 5% larger than a fish aged 20 in 1977. Our study shows that species or populations regarded as relatively insensitive to climate change could still undergo significant changes in growth rate and body size that are likely to have important effects on the productivity and yield of fisheries.