Federated learning has been deployed to train machine learning models from decentralized client data on mobile devices in practice. The clients available for training are observed to have periodically shifting distributions changing with the time of day, which can cause instability in training and degrade the model performance. In this paper, instead of modeling the distribution shift with a block-cyclic pattern as previous works, we model it with a mixture of distributions that gradually changes between daytime modes and nighttime modes, and find this intuitive model to better match the observations in practical federated learning systems. We propose a Federated Expectation-Maximization algorithm enhanced by Temporal priors of the shifting distribution (FedTEM), which jointly learns a mixture model to infer the mode of each client, while training a network with multiple light-weight branches specializing at different modes. Experiments for image classification on EMNIST and CIFAR datasets, and next word prediction on the Stack Overflow dataset show that the proposed algorithm can effectively mitigate the impact of the distribution shift and significantly improve the final model performance.