Image-text pretrained models, e.g., CLIP, have shown impressive general multi-modal knowledge learned from large-scale image-text data pairs, thus attracting increasing attention for their potential to improve visual representation learning in the video domain. In this paper, based on the CLIP model, we revisit temporal modeling in the context of image-to-video knowledge transferring, which is the key point for extending image-text pretrained models to the video domain. We find that current temporal modeling mechanisms are tailored to either high-level semantic-dominant tasks (e.g., retrieval) or low-level visual pattern-dominant tasks (e.g., recognition), and fail to work on the two cases simultaneously. The key difficulty lies in modeling temporal dependency while taking advantage of both high-level and low-level knowledge in CLIP model. To tackle this problem, we present Spatial-Temporal Auxiliary Network (STAN) -- a simple and effective temporal modeling mechanism extending CLIP model to diverse video tasks. Specifically, to realize both low-level and high-level knowledge transferring, STAN adopts a branch structure with decomposed spatial-temporal modules that enable multi-level CLIP features to be spatial-temporally contextualized. We evaluate our method on two representative video tasks: Video-Text Retrieval and Video Recognition. Extensive experiments demonstrate the superiority of our model over the state-of-the-art methods on various datasets, including MSR-VTT, DiDeMo, LSMDC, MSVD, Kinetics-400, and Something-Something-V2. Codes will be available at https://github.com/farewellthree/STAN