Many regions are increasingly threatened by agricultural pests but suffer from a lack of data that hampers the development of adequate population dynamics models that could contribute to pest management strategies. Here, we present a new model relating pest survival to temperature and compare its performance with two published models. We were particularly interested in their ability to simulate the deleterious effect of extreme temperatures even when adjusted to datasets that did not include extreme temperature conditions. We adjusted the models to survival data of three species of potato tuber moth (PTM), some major pests in the Tropical Andes. To evaluate model performance, we considered both goodness-of-fit and robustness. The latter consisted in evaluating their ability to predict the actual altitudinal limits of the species in the Ecuadorian Andes. We found that even though our model did not always provide the best fit to data, it predicted extreme temperature mortality and altitudinal limits accurately and better than the other two models. Our study shows that the ability to accurately represent the physiological limits of species is important to provide robust predictions of invasive pests' potential distribution, particularly in places where temperatures approach lethal extremes. The value of our model lies in its ability to simulate accurate thermal tolerance curves even with small datasets, which is useful in places where adequate pest management is urgent but data are scarce.