Climate change is altering the latitudinal distributions of species, with their capacity to keep pace with a shifting climate depending on the stochastic expression of population growth rates, and the influence of compensatory density feedback on age‐specific survival rates. We use population‐abundance time series at the leading edge of an expanding species’ range to quantify the contribution of stochastic environmental drivers and density feedbacks to the dynamics of life stage‐specific population growth. 2. Using a tropical, range‐shifting Indo‐Pacific damselfish (Abudefduf vaigiensis) as a model organism, we applied variants of the phenomenological Gompertz‐logistic model to a 14‐year dataset to quantify the relative importance of density feedback and stochastic environmental drivers on the separate and aggregated population growth rates of settler and juvenile life stages. 3. The top‐ranked models indicated that density feedback negatively affected the growth of tropical settlers and juveniles. Rates of settlement were negatively linked to temperatures experienced by parents at potential source populations in the tropics, but their subsequent survival and that of juveniles increased with the temperatures experienced at the temperate sink. Including these stochastic effects doubled the deviance explained by the models, corroborating an important role of temperature. By incorporating sea‐surface temperature projections for the remainder of this century into these models, we anticipate improved conditions for the population growth of juvenile coral‐reef fishes, but not for settlers in temperate ecosystems. 4. Previous research has highlighted the association between temperature and the redistribution of species. Our analyses reveal the contrasting roles of different life stages in the dynamics of range‐shifting species responding to climate change, as they transition from vagrancy to residency in their novel ranges.