In recent years, with the advances made in the technology of manufacturing micro systems, the use of these systems has dramatically grown. On the other hand, the use of electro-osmotic as a means for creating flow and improving mixing in microchannels is increasing. In the electro-osmotic flow, a phenomenon known as Joule heating which can play a negative or positive role, depending on the application of the microsystem. Although, the rectangular cross-section is more suitable for microchannel in practice, but this kind of microchannel has not been given proper attention. By comparing DC and alternate electro-osmotic, the use of AC electric field has advantages in some cases. Therefore, in this study, by modeling a rectangular microchannel under an AC electric field, the effect of Joule heating on the distribution of velocity and temperature in the electro-osmotic flow is investigated. By changing the parameters such as the applied voltage to the electrodes, the cross-section dimensions, zeta potential, molar concentration of fluid, fluid type and pressure gradient, results are repoted. The numerical solution is performed by the Fluent software. It is noteworthy that the Poisson-Boltzmann equation is used without the Debye-Huckle approximation for the distribution of electric potential, and because of the dependence of the electric conductivity on temperature, the electric field with constant amplitude is not applied. The results show that by doubling the voltage amplitude, the Joule heating increases so that the temperature in the centerline of the micro-channel from 301.4 Kelvin reaches to 314.6 and when the molar concentration of the fluid increases from to the Joule heating increasing factor of 12.7. This Joule heating can increase the maximum temperature at the midpoint of the microchannel by 15 ? C. Therefore, ignoring the Joule heating and assuming that the constant temperature are not correct. Although the velocity profile changes with increasing the zeta potential and pressure gradient, there is no effect on temperature distribution with respect to the zeta potential. Keywords: Electro-osmotic, Time periodic, Rectangular microchannel, Joule heating, Zeta potential, Electric field