Temporal Domain Generalization (TDG) aims at learning models under temporally evolving data distributions and achieving generalization to unseen future data distributions following the evolving trend. Existing advanced TDG methods learn the evolving patterns through the collective behaviors observed at the population-level of instances, such as time-varying statistics and parameters, tending to overlook the impact of individual-level instance evolving processes on the decision boundary. However, a major obstacle is that datasets at different timestamps may comprise unrelated instances and there is no inherent existence of the instance-level evolving trajectories, which hinders us from learning how the decision boundary changes. To address the above challenges, we propose a Continuous-Time modelling Optimal Transport trajectories (CTOT) framework in this paper. Specifically, we utilize optimal transport to align the data distributions between each pair of adjacent source domains to construct instance evolving trajectories. Subsequently, they are modelled by a continuous-time model and extrapolated to generate future virtual instances, which help the model to adapt its decision boundary to the future domain. Extensive experiments on multiple classification and regression benchmarks demonstrate the effectiveness of the proposed CTOT framework. The code and appendix are both available on https://github.com/JinYujie99/CTOT.