This work aims to * predict * the * 3D * coordinates of the * point * of * interest * (POI) on * the surface of beating heart in dynamic minimally invasive surgery, which can improve the manoeuvrability of cardiac surgical robots and expand their functions. For accurate and robust POI motion prediction, a deep learning technique, the gated recurrent unit (GRU), is employed to learn the spatio-temporal (ST) correlation of the POI and its auxiliary points (APs) from their past trajectories. For reference, two neural network models that exploit only spatial and temporal correlations, respectively, are also investigated. The prediction accuracy and robustness of the above three models are verified based on the motion datasets of phantom and in vivo hearts collected by da Vinci robots. Source codes and motion data are shared on GitHub (https://github.com/oww-file/ST-GRU). The experimental results show that the proposed ST-GRU model is significantly better than the other two reference models, and it outperforms the state-of-the-art deep learning method on the same datasets.