Temperature-jump experiments were carried out on aqueous micellar solutions of hexadecyltrimethylammonium bromide (CTAB) in the presence of potassium bromide (KBr) as a function of the surfactant concentration and the temperature for several salt amounts. The aim was to investigate the kinetics of elongated micelles after a temperature jump in the vicinity of the crossover region between dilute and semidilute regimes using light scattering to probe the relaxation. In the dilute regime one observes a single relaxation phenomenon, wavevector (q) independent, associated with the micellar breaking, whereas in the semidilute concentration range a second one occurs related to the diffusive motion with a shorter, q-dependent, relaxation time. The measured concentration dependences of both relaxation times and amplitudes for 0.15 M salt solutions are in agreement with the theoretical predictions for neutral or highly screened micelles. This is not the case for the 0.1 M KBr micellar solutions where the micellar growth is affected by electrostatic effects. An analysis of the data using the renormalization group theory provides an estimate of the micellar crossover volume fraction between dilute and semidilute regimes. The results are compared to those obtained from light scattering experiments as well as zero-shear viscosity measurements.