This paper presents a new diffeomorphic temporal registration algorithm and its application to motion and strain quantification from a temporal sequence of 3D images. The displacement field is computed by forward eulerian integration of a non-stationary velocity field. The originality of our approach resides in enforcing time consistency by representing the velocity field as a sum of continuous spatiotemporal B-Spline kernels. The accuracy of the developed diffeomorphic technique was first compared to a simple pairwise strategy on synthetic US images with known ground truth motion and with several noise levels, being the proposed algorithm more robust to noise than the pairwise case. Our algorithm was then applied to a database of cardiac 3D+t Ultrasound (US) images of the left ventricle acquired from eight healthy volunteers and three Cardiac Resynchronization Therapy (CRT) patients. On healthy cases, the measured regional strain curves provided uniform strain patterns over all myocardial segments in accordance with clinical literature. On CRT patients, the obtained normalization of the strain pattern after CRT agreed with clinical outcome for the three cases.