In the present paper, closed form solutions for the Nusselt number are obtained for hydrodynamically and thermally fully developed combined electroosmotic and pressure-driven flows in narrow confinements for the constant wall heat flux boundary condition. Overcoming the constraints of the standard models that are valid only within thin electrical double layer (EDL) limits, the effects of thick electric double layers are accounted for as a distinctive feature of this model. Along with Joule heating, viscous dissipation effects, which are particularly important for ultrathin channel dimensions (typically conforming to the cases of thick EDLs), are taken into account. The results are presented in terms of appropriate nondimensional parameters depicting the relative EDL thickness with respect to the channel height, as well as relative strengths of Joule heating and viscous dissipation effects.