Node ranking in temporal networks are often impacted by heterogeneous context from node content, temporal, and structural dimensions. This paper introduces TGNet , a deep-learning framework for node ranking in heterogeneous temporal graphs. TGNet utilizes a variant of Recurrent Neural Network to adapt context evolution and extract context features for nodes. It incorporates a novel influence network to dynamically estimate temporal and structural influence among nodes over time. To cope with label sparsity, it integrates graph smoothness constraints as a weak form of supervision. We show that the application of TGNet is feasible for large-scale networks by developing efficient learning and inference algorithms with optimization techniques. Using real-life data, we experimentally verify the effectiveness and efficiency of TGNet techniques. We also show that TGNet yields intuitive explanations for applications such as alert detection and academic impact ranking, as verified by our case study.