This paper presents a new registration algorithm, called Temporal Diffeomorphic Free Form Deformation (TDFFD), and its application to motion and strain quantification from a sequence of 3D ultrasound (US) images. The originality of our approach resides in enforcing time consistency by representing the 4D velocity field as the sum of continuous spatiotemporal B-Spline kernels. The spatiotemporal displacement field is then recovered through forward Eulerian integration of the non-stationary velocity field. The strain tensor is computed locally using the spatial derivatives of the reconstructed displacement field. The energy functional considered in this paper weighs two terms: the image similarity and a regularization term. The image similarity metric is the sum of squared differences between the intensities of each frame and a reference one. Any frame in the sequence can be chosen as reference. The regularization term is based on the incompressibility of myocardial tissue. TDFFD was compared to pairwise 3D FFD and 3D+t FFD, both on displacement and velocity fields, on a set of synthetic 3D US images with different noise levels. TDFFD showed increased robustness to noise compared to these two state-of-the-art algorithms. TDFFD also proved to be more resistant to a reduced temporal resolution when decimating this synthetic sequence. Finally, this synthetic dataset was used to determine optimal settings of the TDFFD algorithm. Subsequently, TDFFD was applied to a database of cardiac 3D US images of the left ventricle acquired from 9 healthy volunteers and 13 patients treated by Cardiac Resynchronization Therapy (CRT). On healthy cases, uniform strain patterns were observed over all myocardial segments, as physiologically expected. On all CRT patients, the improvement in synchrony of regional longitudinal strain correlated with CRT clinical outcome as quantified by the reduction of end-systolic left ventricular volume at follow-up (6 and 12 months), showing the potential of the proposed algorithm for the assessment of CRT.