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We present a novel dynamic recommendation model that focuses on users who have interactions in the past but turn relatively inactive recently. Making effective recommendations to these time-sensitive cold-start users is critical to maintain the user base of a recommender system. Due to the sparse recent interactions, it is challenging to capture these users' current preferences precisely. Solely relying on their historical interactions may also lead to outdated recommendations misaligned with their recent interests. The proposed model leverages historical and current user-item interactions and dynamically factorizes a user's (latent) preference into time-specific and time-evolving representations that jointly affect user behaviors. These latent factors further interact with an optimized item embedding to achieve accurate and timely recommendations. Experiments over real-world data help demonstrate the effectiveness of the proposed time-sensitive cold-start recommendation model.