Invasive species provide a unique opportunity to evaluate factors controlling biogeographic distributions; we can consider introduction success as an experiment testing suitability of environmental conditions. Predicting potential distributions of spreading species is not easy, and forecasting potential distributions with changing climate is even more difficult. Using the globally invasive coypu (Myocastor coypus [Molina, 1782]), we evaluate and compare the utility of a simplistic ecophysiological based model and a correlative model to predict current and future distribution. The ecophysiological model was based on winter temperature relationships with nutria survival. We developed correlative statistical models using the Software for Assisted Habitat Modeling and biologically relevant climate data with a global extent. We applied the ecophysiological based model to several global circulation model (GCM) predictions for mid-century. We used global coypu introduction data to evaluate these models and to explore a hypothesized physiological limitation, finding general agreement with known coypu distribution locally and globally and support for an upper thermal tolerance threshold. Global circulation model based model results showed variability in coypu predicted distribution among GCMs, but had general agreement of increasing suitable area in the USA. Our methods highlighted the dynamic nature of the edges of the coypu distribution due to climate non-equilibrium, and uncertainty associated with forecasting future distributions. Areas deemed suitable habitat, especially those on the edge of the current known range, could be used for early detection of the spread of coypu populations for management purposes. Combining approaches can be beneficial to predicting potential distributions of invasive species now and in the future and in exploring hypotheses of factors controlling distributions.