Discovering brain mechanisms underlying pain perception remains a challenging neuroscientific problem with important practical applications, such as developing better treatments for chronic pain. Herein, we focus on statistical analysis of functional MRI (fMRI) data associated with pain stimuli. While the traditional mass-univariate GLM  analysis of pain-related brain activation can miss potentially informative voxel interaction patterns, our approach relies instead on multivariate predictive modeling methods such as sparse regression (LASSO  and, more generally, Elastic Net (EN) () that can learn accurate predictive models of pain and simultaneously discover brain activity patterns (relatively small subsets of voxels) allowing for such predictions. Moreover, we investigate the effect of temporal (time-lagged) information, often ignored in traditional fMRI studies, on the predictive accuracy and on the selection of brain areas relevant to pain perception. We demonstrate that (1) Elastic Net regression can be highly predictive of pain perception, by far outperforming ordinary least-squares (OLS) linear regression; (2) temporal information is very important for pain perception modeling and can significantly increase the prediction accuracy; (3) moreover, regression models that incorporate temporal information discover brain activation patterns undetected by non-temporal models.