Video domain adaptation aims to transfer knowledge from labeled source videos to unlabeled target videos. Existing video domain adaptation methods require full access to the source videos to reduce the domain gap between the source and target videos, which are impractical in real scenarios where the source videos are not available with concerns in transmission efficiency or privacy issues. To address this problem, in this paper, we propose to solve a source-free domain adaptation task for videos where only a pre-trained source model and unlabeled target videos are available for learning a multimodal video classification model. Existing source-free domain adaptation methods cannot be directly applied to this task, since videos always suffer from domain discrepancy along both the multimodal and temporal aspects, which brings difficulties in domain adaptation especially when the source data are unavailable. In this paper, we propose a Multimodal and Temporal Relative Alignment Network (MTRAN) to deal with the above challenges. To explicitly imitate the domain shifts contained in the multimodal information and the temporal dynamics of the source and target videos, we divide the target videos into two splits according to the self-entropy values of the classification results. The low-entropy videos are deemed to be source-like while the high-entropy videos are deemed to be target-like. Then, we adopt a self-entropy-guided MixUp strategy to generate synthetic samples and hypothetical samples as instance-level based on source-like and target-like videos, and push each synthetic sample to be similar with the corresponding hypothetical sample that is slightly closer to the source-like videos than the synthetic sample by multimodal and temporal relative alignment schemes. We evaluate the proposed model on four public video datasets. The results show that our model outperforms existing state-of-the-art methods.