Stationary and laminar forced convection in a circular duct is analyzed in the case of a sinusoidal axial change of the wall heat flux such that the modulus of its mean value is either zero or equal to the amplitude. The effect of the axial heat conduction in the fluid is taken into account. Reference is made to the thermally developed region where the temperature distribution can be expressed as the sum of a linear function and a periodic function of the axial coordinate. The temperature field as well as the local and mean Nusselt numbers are evaluated analytically. Comparisons with the solution in the absence of axial heat conduction are performed.