A theoretical analysis is presented to explore the transport characteristics of electro-osmotic flow and associated heat transfer of non-Newtonian power-law fluids in a parallel plate microchannel. The formulation shows that the key parameters governing the current problem include the flow behavior index, the length scale ratio (ratio of Debye length to half channel height), and the Joule heating parameter (ratio of Joule heating to surface heat flux). Analytical expressions are presented for velocity and temperature profiles, the friction coefficient, and the fully developed Nusselt number. In particular, closed-form solutions are obtained for several special values of the flow behavior index. The results reveal that reducing the length scale ratio tends to increase the friction coefficient, and the friction coefficient approaches infinite for slug flow. The increase in the friction coefficient due to increasing the flow behavior index is more noticeable for a smaller length scale ratio. For surface heating, increasing the flow behavior index amplifies the temperature difference between the wall and the fluid, and thus the temperature distribution broadens; while the opposite trend is observed for surface cooling with sufficiently large Joule heating parameter with negative sign. Depending on the value of Joule heating parameter, the fully developed Nusselt number can be either increased or decreased by increasing the flow behavior index and/or the length scale ratio. The effect of flow behavior index on the Nusselt number vanishes as the length scale ratio approaches zero (the limiting case for slug flow).