Reconstructing temporally coherent 3D meshes of the beating heart from multi-view MR images is an important but challenging problem. The challenge is entangled by the complexity in integrating multi-view data, the sparse coverage of a 3D geometry by 2D image slices, and the interplay between geometry and motion. Current approaches often treat mesh reconstruction and motion estimation as two separate problems. Here we propose Mesh4D, a novel motion-aware method that jointly learns cardiac shape and motion, directly from multi-view MR image sequences. The method introduces three key innovations: (1) A cross-attention encoder that fuses multi-view image information, (2) A transformer-based variational autoencoder (VAE) that jointly model the image feature and motion, and (3) A deformation decoder that generates continuous deformation fields and temporally smooth 3D+t cardiac meshes. Incorporating geometric regularisation and motion consistency constraints, Mesh4D can reconstruct high-quality 3D+t meshes (7,698 vertices, 15,384 faces) of the heart ventricles across 50 time frames, within less than 3 s. When compared to existing approaches, Mesh4D achieves notable improvements in reconstruction accuracy and motion smoothness, offering an efficient image-to-mesh solution for quantifying shape and motion of the heart and creating digital heart models.