Emotion dynamics formulates principles explaining the emotional fluctuation during conversations. Recent studies explore the emotion dynamics from the self and inter-personal dependencies, however, ignoring the temporal and spatial dependencies in the situation of multi-modal conversations. To address the issue, we extend the concept of emotion dynamics to multi-modal settings and propose a Dialogue Transformer for simultaneously modeling the intra-modal and inter-modal emotion dynamics. Specifically, the intra-modal emotion dynamics is to not only capture the temporal dependency but also satisfy the context preference in every single modality. The inter-modal emotional dynamics aims at handling multi-grained spatial dependency across all modalities. Our models outperform the state-of-the-art with a margin of 4%-16% for most of the metrics on three benchmark datasets.