Inferring unknown social trust relations attracts increasing attention in recent years. However, social trust, as a social concept, is intrinsically dynamic, and exploiting temporal dynamics provides challenges and opportunities for social trust prediction. In this paper, we investigate social trust prediction by exploiting temporal dynamics. In particular, we model the dynamics of user preferences in two principled ways. The first one focuses on temporal weight; the second one targets temporal smoothness. By incorporating these two types of temporal dynamics into traditional matrix factorization based social trust prediction model, two extended social trust prediction models are proposed and the cor- responding algorithms to solve the models are designed too. We conduct experiments on a real-world dataset and the results dem- onstrate the effectiveness of our proposed new models. Further experiments are also conducted to understand the importance of temporal dynamics in social trust prediction.