For boundary conditions of constant wall temperature, unsteady natural heat transfer at vertical plate have been investigated as numerically. In this study, laminar boundary layer equations have been solved based on Bousinessq assumption. In the computations, Gr and Re numbers have been taken as variables. By using some programs developed for finite difference and finite element codes for the related equations, the velocity and temperature distributions have been obtained. The obtained numerical results were shown with graphics and tables. Results were compared with similarity and integral methods.