The effect of variable thermal conductivity on free-convection boundary layer of an electrically conducting non-Newtonian power law fluid over a nonisothermal vertical full cone in a saturated porous medium in the presence of a magnetic field applied normal to the cone surface has been studied. The transformed nonlinear ordinary differential equations are solved numerically using the fourth order Runge-Kutta method coupled with the shooting method. The effects of the power law index, the magnetic parameter and the thermal conductivity parameter on the temperature profiles as well as on the local Nusselt number are presented and discussed.