Transient heat transfer solutions are found for a fluid flowing within a parallel plate duct when there is sinusoidal generation with axial position in the duct wall. Solutions are found for wall temperature, surface heat flux and fluid bulk mean temperature as a function of position and time in this conjugated problem. To develop this solution, finite difference methods are used as well as the quasi-steady method and another method which employs a two integral representation for the surface heat flux. Accuracy limitations of the quasi-steady results are identified. Transient local Nusselt number predictions show its dependence upon time.