The present investigation considers the fully developed electro-osmotic flow of power-law fluids in a planar microchannel subject to constant wall heat fluxes. Using an approximate velocity distribution, closed form expressions are obtained for the transverse distribution of temperature and Nusselt number. The approximate solution is found to be quite accurate, especially for the values of higher than ten for the dimensionless Debye-Huckel parameter where the exact values of Nusselt number are predicted. The results demonstrate that a higher value of the dimensionless Debye-Huckel parameter is accompanied by a higher Nusselt number for wall cooling, whereas the opposite is true for wall heating case. Although to increase the dimensionless Joule heating term is to decrease Nusselt number for both pseudoplastic and dilatant fluids, nevertheless its effect on Nusselt number is more pronounced for dilatants. Furthermore, to increase the flow behavior index is to decrease the Nusselt number for wall cooling, whereas the contrary is right for the wall heating case. Depending on the value of flow parameters, a singularity is observed in the Nusselt number values of the wall heating case.