We analyse the linear and weakly nonlinear thermoconvective stability of a ferrofluid, confined between rigid horizontal plates at different temperatures and subjected to a strong uniform external magnetostatic field in the vertical direction. When this magnetically saturated ferrofluid is heated from below our critical parameters for the linear stability problem agree with those of Finlayson. The corresponding weakly nonlinear analysis predicts that under microgravity conditions, the ratio of the steady heat transfer by convection to that by conduction can be up to 10% greater than when the magnetic field is absent. If the ferrofluid is heated from above, critical temperature gradients can attain extremely high values and the horizontal separation of roll cells can be less than half the spacing observed when the lower plate is warmer. In this non-standard regime, where convection is due to magnetic body forces, the Nusselt numbers for a given supercritical temperature gradient are significantly higher than when the ferrofluid is heated from below.