Cell polarity underlies many aspects of metazoan development and homeostasis, and relies notably on a set of PAR proteins located at the cell cortex. How these proteins interact in space and time remains incompletely understood. We performed a quantitative assessment of polarity establishment in one-cell stage Caenorhabditis elegans embryos by combining time-lapse microscopy and image analysis. We used our extensive data set to challenge and further specify an extant mathematical model. Using likelihood-based calibration, we uncovered that cooperativity is required for both anterior and posterior PAR complexes. Moreover, we analyzed the dependence of polarity establishment on changes in size or temperature. The observed robustness of PAR domain dimensions in embryos of different sizes is in agreement with a model incorporating fixed protein concentrations and variations in embryo surface/volume ratio. In addition, we quantified the dynamics of polarity establishment over most of the viable temperatures range of C. elegans. Modeling of these data suggests that diffusion of PAR proteins is the process most affected by temperature changes, although cortical flows appear unaffected. Overall, our quantitative analytical framework provides insights into the dynamics of polarity establishment in a developing system.