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Cold-start recommendation is one of the major challenges faced by recommender systems (RS). Herein, we focus on the user cold-start problem. Recently, methods utilizing side information or meta-learning have been used to model cold-start users. However, it is difficult to deploy these methods to industrial RS. There has not been much research that pays attention to the user cold-start problem in the matching stage. In this paper, we propose Cold & Warm Net based on expert models who are responsible for modeling cold-start and warm-up users respectively. A gate network is applied to incorporate the results from two experts. Furthermore, dynamic knowledge distillation acting as a teacher selector is introduced to assist experts in better learning user representation. With comprehensive mutual information, features highly relevant to user behavior are selected for the bias net which explicitly models user behavior bias. Finally, we evaluate our Cold & Warm Net on public datasets in comparison to models commonly applied in the matching stage and it outperforms other models on all user types. The proposed model has also been deployed on an industrial short video platform and achieves a significant increase in app dwell time and user retention rate.