Recommender systems that can learn from cross-session data to dynamically predict the next item a user will choose are crucial for online platforms. However, existing approaches often use out-of-the-box sequence models which are limited by speed and memory consumption, are often infeasible for production environments, and usually do not incorporate cross-session information, which is crucial for effective recommendations. Here we propose Hierarchical Temporal Convolutional Networks (HierTCN), a hierarchical deep learning architecture that makes dynamic recommendations based on users' sequential multi-session interactions with items. HierTCN is designed for web-scale systems with billions of items and hundreds of millions of users. It consists of two levels of models: The high-level model uses Recurrent Neural Networks (RNN) to aggregate users' evolving long-term interests across different sessions, while the low-level model is implemented with Temporal Convolutional Networks (TCN), utilizing both the long-term interests and the short-term interactions within sessions to predict the next interaction. We conduct extensive experiments on a public XING dataset and a large-scale Pinterest dataset that contains 6 million users with 1.6 billion interactions. We show that HierTCN is 2.5x faster than RNN-based models and uses 90% less data memory compared to TCN-based models. We further develop an effective data caching scheme and a queue-based mini-batch generator, enabling our model to be trained within 24 hours on a single GPU. Our model consistently outperforms state-of-the-art dynamic recommendation methods, with up to 18% improvement in recall and 10% in mean reciprocal rank.