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Forecasting invasion risk under future climate conditions is critical for the effective management of invasive species, and species distribution models (SDMs) are key tools for doing so. However, SDM‐based forecasts are uncertain, especially when correlative statistical models extrapolate to nonanalog environmental domains, such as future climate conditions. Different assumptions about the functional form of the temperature–suitability relationship can impact predicted habitat suitability under novel conditions. Hence, methods to understand the sources of uncertainty are critical when applying SDMs. Here, we use high‐resolution predictions of lake water temperatures to project changes in habitat suitability under future climate conditions for an invasive macrophyte (Myriophyllym spicatum). Future suitability was predicted using five global circulation models and three statistical models that assumed different species–temperature functional responses. The suitability of lakes for M. spicatum was overall predicted to increase under future climate conditions, but the magnitude and direction of change in suitability varied greatly among lakes. Variability was most pronounced for lakes under nonanalog temperature conditions, indicating that predictions for these lakes remained highly uncertain. Integrating predictions from SDMs that differ in their species–environment response function, while explicitly quantifying uncertainty across analog and nonanalog domains, can provide a more robust and useful approach to forecasting invasive species distribution under climate change. [ABSTRACT FROM AUTHOR]