We provide a numerical analysis of three-dimensional free convection of a liquid in a Rayleigh-Bénard configuration, subject to a steady and uniform magnetic field, using the finite volume code Jadim. The influence of the Hartmann and Rayleigh numbers are studied. We compare our results to several experimental works. As suggested by previous experiments, the magnetic field tends to lower the heat transfer at the walls. This is caused by a significant alteration of the flow structures, due to the Lorentz force. For slightly overcritical Rayleigh numbers, two-dimensional rolls appear but the flow structure rapidly becomes three-dimensional as we increase the Rayleigh number. The magnetic field tends to destroy those structures and the transition to a 3D flow is delayed to higher values of the Rayleigh number, when the Hartmann number is increased. We show that the averaged heat transfer at the walls decreases, although it remains of the same order of magnitude. However the local structure of heat transfer is altered.