Unilamellar vesicles are observed to form in aqueous solutions of the cationic surfactant, cetyl trimethylammonium bromide (CTAB), when 5-methyl salicylic acid (5mS) is added at slightly larger than equimolar concentrations. When these vesicles are heated above a critical temperature, they transform into long, flexible wormlike micelles. In this process, the solutions switch from low- viscosity, Newtonian fluids to viscoelastic, shear-thinning fluids having much larger zero-shear viscosities (e. g., 1000-fold higher). The onset temperature for this transition increases with the concentration of 5mS at a fixed CTAB content. Small-angle neutron scattering (SANS) measurements show that the phase transition from vesicles to micelles is a continuous one, with the vesicles and micelles coexisting over a narrow range of temperatures. The tunable vesicle-to-micelle transition and the concomitant viscosity increase upon heating may have utility in a range of areas, including microfluidics, controlled release, and tertiary oil recovery.