The kinetics of the sphere-to-rod transition was studied in aqueous micelle solutions of triblock copolymer poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) pluronic P103 (PEO17PPO60PEO17). This transition was triggered by a temperature jump from the sphere phase to the rod phase and monitored with dynamic light scattering. The combination of the scattering intensity and the hydrodynamic radius were used to show that the micelles grow steadily as rods throughout the growth process. The transition was found to exhibit a single exponential behavior even in the case of large deviations from equilibrium. The linear increase in the decay rate with increasing copolymer concentration shows that the transition is dominated by a mechanism involving fusion and fragmentation of proper micelles. The decays of the sphere-to-rod transition were simulated for two pathways: random fusion fragmentation and successive addition of spherical micelles to rods. We show that micelle growth most likely occurs via random fusion-fragmentation. The second order rate constant for fusion and the fragmentation rate are calculated for the case of random fusion-fragmentation.