We present an experimental study of nonlinear lensing ofnear-resonant light by a cloud of laser-cooled rubidium atoms,specifically aimed at understanding the role of the interactiontime between the light and the atomic vapor. We identify fourdifferent nonlinear mechanisms, each associated with a differenttime constant: electronic nonlinearity, Zeeman optical pumping,hyperfine optical pumping and radiation pressure. Our observationscan be quite accurately reproduced using a simple rate equationmodel which allows for a straightforward discussion of the variouseffects. The results are important for planningmore refined experiments on transverse nonlinear optics andself-organization in samples of cold atoms.