To quantify and explore the role of temperature on population outbreaks of a nonindigenous bryozoan (Membranipora membranacea) in kelp beds in the western North Atlantic (Nova Scotia, Canada), we constructed an individual‐based model using field‐derived estimates for temperature‐dependent colony settlement and growth. Using temperature as the single input variable, the model successfully simulated the timing of onset of settlement, colony abundance, colony size, and coverage on kelps. We used the model to examine the relative effect on the population of varying temperature by ‐2°C to +2°C each day. The timing of onset of settlement varied by 18°C−1 with changes in temperature from January to August. Variations in temperature had nonlinear effects on the population, with an increase in daily temperature of 1°C and 2°C causing the cover of colonies on kelps to increase by factors of 9 and 62, respectively. Changes in winter and spring temperature had the most pronounced effects on the timing and abundance of colonies, while changes in summer temperature had the most pronounced effect on colony size and coverage on kelp blades. Outbreaks of this species will increase in frequency and intensity if temperatures warm as a result of climate change, causing defoliation of kelp beds and, thus, facilitating the invasion of other nonindigenous benthic species.