A numerical methodology is developed to predict kinematic and thermal characteristics of a bidimensional, laminar and permanent flow in a sinusoidal duct. The basis of the method is an algebraic coordinate transformation which maps the complex fluid domain onto a rectangle. The results for the central area, where the flow is periodic and fully developed show a deformation of the streamlines and recirculation zones in highly curved regions. The average Nusselt number is found to be an increasing function of the Reynolds and Prandtl numbers, and of the amplitude and the height of the duct.