The stream function-vorticity formulation is a useful alternative to solving the Navier-Stokes equations in two dimensional domain. One of its major difficulties is the lack of boundary conditions for vorticity, and several schemes are proposed to satisfy such a condition. In this paper we propose a finite element scheme for solving the couple problem of the stream function-vorticity formulation using linear triangle elements. A possible application of the method is also demonstrated using the calculated velocity field from the formulation in the heat transport equation to study the temperature distribution in a incompressible single-phase fluid medium. The results obtained were satisfactory when using low to moderate Reynolds number.