The electro-osmotic flow (EOF) and associated heat transfer are investigated in a semi-annular microcapillary. The potential, velocity, and temperature fields are solved by analytic approaches including the eigenfunction expansion and the Green’s function methods. By selecting the potential sign of each surface of the channel, the bulk fluid may flow in two opposite directions. Effects of the key parameters governing the problem are examined. The mass flow rate increases when the hydraulic diameter is increased or the electrokinetic radius is decreased. The results reveal that surface cooling and/or surface heating (of the inner or outer walls) strongly affects the fluid temperature distributions as well as the position of the maximum/minimum temperature region inside the domain; the latter indicates temperature gradients in fluid. Also, higher thermal scale ratio leads to broaden the temperature distribution. Depending on the value of the geometric radius ratio (and for all values of the thermal scale ratio), the fully developed Nusselt number approaches a specific value as the electrokinetic radius tends to infinity.