Leveraging temporal information has been regarded as essential for developing video understanding models. However, how to properly incorporate temporal information into the recent successful instance discrimination based contrastive self-supervised learning (CSL) framework remains unclear. As an intuitive solution, we find that directly applying temporal augmentations does not help, or even impair video CSL in general. This counter-intuitive observation motivates us to re-design existing video CSL frameworks, for better integration of temporal knowledge. To this end, we present Temporal-aware Contrastive self-supervised learningTaCo, as a general paradigm to enhance video CSL. Specifically, TaCo selects a set of temporal transformations not only as strong data augmentation but also to constitute extra self-supervision for video understanding. By jointly contrasting instances with enriched temporal transformations and learning these transformations as self-supervised signals, TaCo can significantly enhance unsupervised video representation learning. For instance, TaCo demonstrates consistent improvement in downstream classification tasks over a list of backbones and CSL approaches. Our best model achieves 85.1% (UCF-101) and 51.6% (HMDB-51) top-1 accuracy, which is a 3% and 2.4% relative improvement over the previous state-of-the-art.