Mixed convection flow in a vertical circular duct subjected to a periodic sinusoidal temperature change at the wall is investigated. The analysis is performed by considering fully-developed parallel flow and steady-periodic regime. The local momentum and energy balance equations, together with the constraint equations which arise from the definition of mean velocity and mean temperature, are written in a dimensionless form and mapped into equations in the complex domain. One obtains two independent boundary value problems, which provide the mean value and the oscillating term of the velocity and temperature distributions. These boundary value problems are solved analytically, and the velocity and temperature distributions are obtained as functions of three parameters: the Prandtl number, Pr, the dimensionless frequency Ω , the ratio between the Grashof number Gr and the Reynolds number Re. The Fanning friction factor and the dimensionless heat flux are evaluated.