Convection flow in a vertical layer of ferrofluid heated from a side and subject to the transverse magnetic field is studied. A stability map is computed and compared with experimental flow visualizations. It is shown that the excitation of magneto-convection leads to the formation of vertically aligned rolls. The interaction of thermo-gravitational and thermo-magnetic motions results in roll and wave patterns of various spatial orientations. A new thermo-magnetic wave instability mechanism is found to exist for sufficiently large values of magnetic Grashof number.