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In sparse recommender settings, users' context and item attributes play a crucial role in deciding which items to recommend next. Despite that, recent works in sequential and time-aware recommendations usually either ignore both aspects or only consider one of them, limiting their predictive performance. In this paper, we address these limitations by proposing a context and attribute-aware recommender model (CARCA) that can capture the dynamic nature of the user profiles in terms of contextual features and item attributes via dedicated multi-head self-attention blocks that extract profile-level features and predicting item scores. Also, unlike many of the current state-of-the-art sequential item recommendation approaches that use a simple dot-product between the most recent item's latent features and the target items embeddings for scoring, CARCA uses cross-attention between all profile items and the target items to predict their final scores. This cross-attention allows CARCA to harness the correlation between old and recent items in the user profile and their influence on deciding which item to recommend next. Experiments on four real-world recommender system datasets show that the proposed model significantly outperforms all state-of-the-art models in the task of item recommendation and achieving improvements of up to 53% in Normalized Discounted Cumulative Gain (NDCG) and Hit-Ratio. Results also show that CARCA outperformed several state-of-the-art dedicated image-based recommender systems by merely utilizing image attributes extracted from a pre-trained ResNet50 in a black-box fashion.