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An important goal of cognitive brain imaging studies is to model the functional organization of the brain; yet there exists currently no functional brain atlas built from existing data. One of the main roadblocks to the creation of such an atlas is the functional variability that is observed in subjects performing the same task; this variability goes far beyond anatomical variability in brain shape and size. Functionbased alignment procedures have recently been proposed in order to improve the correspondence of activation patterns across individuals. However, the corresponding computational solutions are costly and not wellprincipled. Here, we propose a new framework based on optimal transport theory to create such a template. We leverage entropic smoothing as an efficient means to create brain templates without losing fine-grain structural information; it is implemented in a computationally efficient way. We evaluate our approach on rich multi-subject, multi-contrasts datasets. These experiments demonstrate that the template-based inference procedure improves the transfer of information across individuals with respect to state of the art methods.