The present study considers both the hydrodynamic and thermal characteristics of combined electroosmotic and pressure driven flow in a microannulus. Analytical solutions are presented using the Debye–Hückel linearization along with the uniform Joule heating and negligible viscous dissipation assumptions, whereas exact results are achieved numerically. Here, the range of validity for the Debye–Hückel linearization is found to be about two times of that for a parallel plate microchannel. Accordingly, this linearization may successfully be used to evaluate the potential and velocity distributions up to the zeta potentials of 100 mV, provided that the dimensionless Debye–Hückel parameter is above 10; nevertheless, the calculated wall shear stresses may be significantly different from the exact ones, even for lower zeta potentials. The viscous heating effects are found to be limited to low values of the dimensionless Debye–Hückel parameter. These effects are pronounced in the presence of a favorable pressure gradient, whereas the opposite is true for an opposed pressure gradient. Furthermore, the influence of increasing the annular geometry parameter, that is the inner to outer radii ratio, generally is to decrease both the inner and outer Nusselt numbers. It is also revealed that the pressure effects vanish at higher values of this parameter.