Temporal graphs are widespread in real-world applications such as social networks, as well as trade and transportation networks. Predicting dynamic links within these evolving graphs is a key problem. Many memory-based methods use temporal interaction histories to generate node embeddings, which are then combined to predict links. However, these approaches primarily focus on individual node representations, often overlooking the inherently pairwise nature of link prediction. While some recent methods attempt to capture pairwise features, they tend to be limited by high computational complexity arising from repeated embedding calculations, making them unsuitable for large-scale datasets like the Temporal Graph Benchmark (TGB). To address the critical need for models that combine strong expressive power with high computational efficiency for link prediction on large temporal graphs, we propose Temporal Neural Common Neighbor (TNCN). Our model achieves this balance by adapting the powerful pairwise modeling principles of Neural Common Neighbor (NCN) to an efficient temporal architecture. TNCN improves upon NCN by efficiently preserving and updating temporal neighbor dictionaries for each node and by using multi-hop common neighbors to learn more expressive pairwise representations. TNCN achieves new state-of-the-art performance on Review from five large-scale real-world TGB datasets, 6 out of 7 datasets in the transductive setting and 3 out of 7 in the inductive setting on small- to medium-scale datasets. Additionally, TNCN demonstrates excellent scalability, outperforming prominent GNN baselines by up to 30.3 times in speed on large datasets. Our code is available at https://github.com/GraphPKU/TNCN.