In this paper, we propose a novel Temporal Sequence-Aware Model (TSAM) for few-shot action recognition (FSAR), which incorporates a sequential perceiver adapter into the pre-training framework, to integrate both the spatial information and the sequential temporal dynamics into the feature embeddings. Different from the existing fine-tuning approaches that capture temporal information by exploring the relationships among all the frames, our perceiver-based adapter recurrently captures the sequential dynamics alongside the timeline, which could perceive the order change. To obtain the discriminative representations for each class, we extend a textual corpus for each class derived from the large language models (LLMs) and enrich the visual prototypes by integrating the contextual semantic information. Besides, We introduce an unbalanced optimal transport strategy for feature matching that mitigates the impact of class-unrelated features, thereby facilitating more effective decision-making. Experimental results on five FSAR datasets demonstrate that our method set a new benchmark, beating the second-best competitors with large margins.