Compositional Zero-Shot Learning (CZSL) aims to recognize novel attribute-object compositions based on the knowledge learned from seen ones. Existing methods suffer from performance degradation caused by the distribution shift of label space at test time, which stems from the inclusion of unseen compositions recombined from attributes and objects. To overcome the challenge, we propose a novel approach that accumulates comprehensive knowledge in both textual and visual modalities from unsupervised data to update multimodal prototypes at test time. Building on this, we further design an adaptive update weight to control the degree of prototype adjustment, enabling the model to flexibly adapt to distribution shift during testing. Moreover, a dynamic priority queue is introduced that stores high-confidence images to acquire visual prototypes from historical images for inference. Since the model tends to favor compositions already stored in the queue during testing, we warm-start the queue by initializing it with training images for visual prototypes of seen compositions and generating unseen visual prototypes using the mapping learned between seen and unseen textual prototypes. Considering the semantic consistency of multimodal knowledge, we align textual and visual prototypes by multimodal collaborative representation learning. To provide a more reliable evaluation for CZSL, we introduce a new benchmark dataset, C-Fashion, and refine the widely used but noisy MIT-States dataset. Extensive experiments indicate that our approach achieves state-of-the-art performance on four benchmark datasets under both closed-world and open-world settings. The source code and datasets are available at https://github.com/xud-yan/WARM-CAT .