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Molecular-dynamics simulations of the (0001) surface of ${\mathrm{Cr}}_{2}{\mathrm{O}}_{3}$ were carried out in the [300--2800 K] range of temperatures using a classical Pauling-type pair potential. The analysis of the structural data shows a strong surface relaxation in agreement with experiment. Both static and dynamic surface properties indicate that a surface melting process occurs well below the melting point, which is estimated to be about 2500 K, in excellent agreement with the experimental value of 2556 K. The diffusive properties of this disordered phase are described and it is found that the main mechanism for diffusion involves hopping of surface atoms.