We have studied the kinetics of the solubilization of oil through a temperature jump into a droplet microemulsion phase in the system water-pentaethylene oxide dodecyl ether-decane at 25 degreesC. The initial state is formed by subjecting the equilibrium system at 25 degreesC to a temperature quench to 22, 20, and 14 degreesC, respectively. At this lower temperature, which at equilibrium corresponds to a two-phase system, oil droplets form and grow in size with increasing time. By varying the time between the quench and the T-jump, the size of the initial oil drops is varied in a systematic and known way in the relaxation study. The relaxation process is monitored by following the turbidity of the system. We find that for all the systems the relaxation back to equlibrium is much faster than the drop growth process observed after the temperature quench. This general observation is explained by realizing that the redissolution of the oil drops is analogous to the oil transfer phase, which in the quench experiment occurs prior to the Ostwald ripening phase. More significant is that we observed a qualitative transition in the relaxation behavior when the initial aggregate distribution is varied. In all cases we have the same initial temperature and overall composition and one population of many small droplets and fewer larger drops. The size of the larger drops only affects the relaxation in a quantitative way. if the small droplets are only slightly smaller than the equilibrium size, equilibration occurs through the diffusion of oil molecules in the bulk phase. When the initial droplets are sufficiently small, a new kinetic route is available where there is an efficient direct oil transfer between the small droplets and large drops. This allows for a fast relaxation of the oil distribution between the two populations of drops.