An inverse variational finite element model is developed for the purpose of estimating ocean surface velocity fields from sequences of temperature fields. The cross-isotherm component of the velocity is controlled by a mixed layer integrated formulation of the heat balance. The aperture problem imposes additional constraints on the flow field: we control the divergence and the vorticity of the horizontal velocity. The method is then applied to sequences of sea surface temperature (SST) fields from a fine-mesh numerical simulation over the Brazil-Malvinas Confluence region. The difference between the actual velocity and the SST inverted velocity is 11% rms in magnitude and 17¿ rms in direction. These differences are analyzed; divergence and vorticity are computed. The hypothesis of neglecting the source terms made in the formulation of the mixed layer integrated heat balance is verified. The sensitivity of the solution to the influence of the constraints is examined. Perturbations are performed yielding fields of ellipses of covariance. We obtain on average 15% uncertainties in magnitude and 25¿ in direction of the velocity. Differences between the actual and SST inverted velocities fall into those covariance ellipses, except over regions where temperature does not change from one image to the other. ¿ 2000 American Geophysical Union