The new method based on positron annihilation lifetime spectroscopy (PALS) to determine both the mean core radius, R(core), and aggregation number, N(ag), of micelles is applied to the study of aqueous solutions of the triblock Pluronic P84 copolymer as a function of temperature (T), beyond the gelification point (334 K). Two long-lived components appear in the PALS spectra, ascribed to triplet positronium in the water bulk (o-Ps(aq)) and in the organic core of the micelles (o-Ps(org)). Of the various fitting parameters, only the lifetime of the latter species, tau4, and the micellar parameters, R(core) and N(ag), disclose the occurrence of gelification by first increasing up to 334 K, then decreasing. By contrast to what is known in case of phase transition, none of the parameters shows any abrupt change at 334 K, whereas the macroscopic viscosity of the solutions suffers a drastic increase. This is attributed to the fact that positronium is sensitive to the microviscosity of the solutions. At the transition point, the properties of the polyoxipropylene aggregates forming the organic core of the P84 micelles are not greatly affected. Furthermore, the fact that the experimental N(ag) values coincide with those calculated for spheres, from the R(core) values, indicates that the shape of the P84 cores does not change significantly after gelification. The onset of gelification results from a decrease in the hydrogen bonding interactions in the solution with an ensuing relative increase in the interactions between the polyoxipropylene (PPO) groups, initially forming the corona of the P84 micelles, in an intermicellar mode. This increased solicitation of the PPO groups outside their initial location would result in depletion in the number of surfactant molecules forming the micelles, viz. a decrease in both R(core) and N(ag) above 334 K. From the data, additional information can be gained regarding the local viscosity and surface tension in the micellar cores.