Rheological experiments were carried out on aqueous micellar solutions of the "dimeric" surfactant ethanediyl-alpha,omega-bis(dodecyldimethylammonium bromide) as a function of surfactant volume fraction and temperature. The aim was to investigate the effect of electrostatic interactions on the micellar size through the linear viscoelastic properties of the system. The zero-shear viscosity results indicate a sharp crossover from a dilute regime in which the micelle growth is very weak to a regime of rapid growth, in agreement with the theoretical predictions. However, upon increasing further the volume fraction, a maximum of the zero-shear viscosity is observed which suggests that the micellar length also goes through a maximum. This is confirmed by the analysis of the viscoelastic spectra on the basis of the recently developed models taking into account both reptation and Rouse processes. The decrease of micellar length observed in the high volume fraction range has been interpreted as due to the decrease of the effective end-cap energy associated with the theoretically predicted increase of the micelle ionization degree with volume fraction. The effect of the electrostatic interactions also appears in the behavior of the plateau modulus that exhibits a larger volume fraction dependence than in highly screened micelles.