Natural convection in a melting material (hexadecane) is studied experimentally using Magnetic Resonance Imaging. This imaging technique allows to discriminate solid and liquid phases and to measure velocity vectors in the volume sample, even through/in opaque phases. Within our experimental conditions, the convection occurs above Ra ≈ 1430. The thermo-convective flow affects the melting interface leading to higher liquid height in uprising flow and lower liquid height in downward flow regions. Our experiments show that (i) the transient evolution of the mean liquid height ̅h is enhanced with convection since ̅h ∝ t^0.8 ( ̅h ∝t^(1/(2-3β)) with β=1/4), while ̅h ∝ t^0.5 in the conductive regime similarly to the Stefan's problem; (ii) the steady averaged liquid height ̅h increases 4 times larger in the convective regime than in the conductive regime. In our experiments the range of A, ratio between the solid and liquid heights, is such as A>1.5. Within this range of values we obtain convective pattern under the form of hexagons / polygons. As the melting boundary grows, we observe a decrease in the polygon number. The polygonal pattern is characterized by a constant dimensionless wavelength, i.e. λ / ̅h ∝ 2, and thus a constant wavenumber around 3.1 similarly to the primary bifurcation in the classical Rayleigh-Bénard Convection (RBC). Heat transfer is evaluated via the Nusselt number Nu. Close to the onset of convection and above, our results highlight a scaling law Nu∝ Ra^β with β=1/4 similarly to the classical RBC. The kinetic energy E_c is also evaluated via velocity measurements leading to E_c/E_0 ∝ Nu^4 and therefore to Re∝ Ra^2β ∝ Ra^1/2. Within the frame of our experiments, all scaling laws are converging to β=1/4. They reflect clearly an increase in the convective intensity from both thermal and dynamical points of view.