MHD natural convection flow of an electrically conducting fluid along a vertical flat plate with temperature dependent thermal conductivity and conduction effects is analyzed. The governing equations with associated boundary conditions for this phenomenon are converted to dimensionless forms using a suitable transformation. The transformed non-linear equations are then solved using the implicit finite difference method with Keller-box scheme. Numerical results of the velocity, temperature, skin friction coefficient and surface temperature for different values of the magnetic parameter, thermal conductivity variation parameter, Prandtl number and conjugate conduction parameter are presented graphically. Detailed discussion is given for the effects of the aforementioned parameters.