A finite element method is used to study the heat-transfer response of an incompressible, laminar, transient free convection flow over a semi-infinite vertical plate. The non-dimensional governing equations are solved by the finite element method (FEM). The resulting non-linear integral equations are linearized and solved using the Newton–Raphson iteration. The resulting first-order ordinary differential equations with respect to time are solved using the implicit Euler scheme. Numerical results for the details of the velocity and temperature contours and profiles as well as heat transfer rate in terms of Nusselt number which are shown on graphs have been presented.