Cross-domain sequential recommendation (CDSR) aims to predict user-item interactions from historical sequences across domains. Current CDSR approaches mainly focus on leveraging intrinsic connections among items to capture the dependencies across domains for representation learning. However, these approaches still exist major limitations, including: (1) Extensive CDSR methods overlook temporal dynamics, failing to utilize evolving sequential patterns of user-item interactions. (2) Irrelevant features from source domain to target domain lead to negative transfer of user preferences. To overcome these challenges, we propose an innovative Cross-Domain Sequential Recommendation with Temporal Encoding and Projection-based Learning (TP-CDSR). It features a temporal encoding module that captures the evolving sequences of user interactions by considering the temporal effects as kernels. The projection mechanism learns domain-specific matrices to map the user and item representations across domains, which can reduce migration of redundant features. Comprehensive experiments on two real datasets confirm that TP-CDSR achieves superior results compared to various state-of-the-art recommendation algorithms.