Calculations are presented of the magneto-hydrodynamic response of a planar target to nonuniformities in energy deposition by a laser. The amplitude of the nonuniformities are assumed small and the equations are linearised in small perturbations about the solution for steady planar ablation driven by uniform laser energy deposition. The grad(n)xgrad(T) magnetic field source is included, along with Nernst convection and the Righi-Leduc heat flow. The magnetic field is shown to give a small increase in smoothing. A source term for magnetic field is induced to simulate the effects of the Weibel instability. The instability is not strong enough to overcome the smoothing processes under the present assumptions.