In this paper, a numerical study of heat transfer by natural convection along a wavy vertical plate with variable wall temperature is presented. The numerical method is applied to obtain the analytic solution. The homotopic transformation is employed to transform the physical domain into a flat plate. The boundary layer equations and the boundary conditions are discretized by the finite difference scheme and solved numerically using the method of Gauss-Seidel algorithm with relaxation coefficient. Effects of the wavy geometry and the constant m (m ≥ 0) on the velocity profiles, temperature profiles, local Nusselt number and   skin friction coefficient are presented and discussed in detail. Results show that increasing of the constant m leads to increase the heat transfer rate, while the high amplitude wavelength rates reduce in general the heat transfer.