A new model is set up to represent the effect of temperature and light on microalgae growth, and predict the productivity of outdoor microalgae based processes. This model includes three cardinal temperatures (T-min, T-opt, and T-max) and three parameters associated to the light response (mu(max), l(opt), and alpha). These six parameters have a clear biological meaning which makes model calibration straightforward. An algorithm to estimate both the model parameters and their associated confidence regions is developed. Results show that this model can successfully represent experimental data sets from 15 species cultivated in different experimental conditions. The model predictions, when compared to realistic temperatures recorded in outdoor photobioreactors or raceways, point out a strong decrease of productivity due to over-warming for most commercial species. (C) 2012 Elsevier Ltd. All rights reserved.