Financial risk prediction plays an important role in financial market regulation and financial investment, and has become a research hotspot in artificial intelligence and financial technology in recent years. Due to the complex investment, supply and other relationships among financial event entities, existing research on financial risk prediction often employs various static and dynamic graph structures to model the relationship among financial entities. Meanwhile, convolutional graph neural networks and other methods are adopted to embed relevant graph structure information into the feature representation of financial entities, which enables the representation of both semantic and structural information related to financial risks. However, previous reviews of financial risk prediction only focus on studies based on static graph structures, but ignore the characteristics that the relationship among entities in financial events will change dynamically over time, which reduces the accuracy of risk prediction results. With the development of temporal graph neural networks, increasingly more studies have begun to pay attention to financial risk prediction based on dynamic graph structures, and a systematic and comprehensive review of these studies will help learners foster a complete understanding of financial risk prediction research. According to different methods to extract temporal information from dynamic graphs, this study first reviews three different neural network models for temporal graphs. Then, based on different graph learning tasks, it introduces the research on financial risk prediction in four areas, including stock price trend risk prediction, loan default risk prediction, fraud transaction risk prediction, and money laundering and tax evasion risk prediction. Finally, the difficulties and challenges facing the existing temporal graph neural network models in financial risk prediction are summarized, and potential directions for future research are prospected.