We analyze linear and weakly nonlinear thermoconvective stability in a thin layer of ferrofluid confined between rigid horizontal plates at different temperatures and subjected to a weak uniform external magnetic field in the vertical direction. When the ferrofluid is heated from below the critical gravitational and magnetic Rayleigh numbers and the critical horizontal wavenumber of the roll cells agree with those of Finlayson. In this case the weakly nonlinear analysis predicts that the ratio of the steady heat transfer by convection to that by conduction increases by some 10% as the gravitational Ralyeigh number falls from its normal terrestrial value of 1707.8 to 0. This enhancement in the convective heat transfer declines as the magnetic susceptibility of the ferrofluid increases. If the ferrofluid layer is heated from above the gravitational Rayleigh number becomes negative, the ratio of convective to conductive heat fluxes can greatly exceed 10%, and the magnitudes of the critical horizontal wavenumbers are substantially higher than those when the ferrofluid is heated from below.