Thermal rectification of far-field heat currents is experimentally demonstrated by exploiting the metal-insulator transition of ${\mathrm{VO}}_{2}$ driving the significant temperature variations of its emissivity, within a narrow interval of temperatures. This is achieved by measuring remarkable differences on the radiative heat flux between a ${\mathrm{VO}}_{2}$ film placed in vacuum and in front of a heat fluxmeter, when their temperature difference is reversed. By testing three ${\mathrm{VO}}_{2}$ films deposited on a substrate of $r$-sapphire, $c$-sapphire, and silicon, the highest rectification factor of $61\mathrm{%}$ is obtained for the first film operating with a temperature difference of ${40}^{\ensuremath{\circ}}\mathrm{C}$ with respect to the fluxmeter. This rectification factor is higher than or comparable to the respective ones reported in the literature for near- or far-field radiative diodes subjected to a temperature difference of ${70}^{\ensuremath{\circ}}\mathrm{C}$ between their terminals. This experimental value is consistent with the theoretical one predicted by an analytical expression derived for the maximum rectification factor, as a function of the ${\mathrm{VO}}_{2}$ emissivity in the metallic and insulating phases, sensor emissivity, and geometrical parameters. The obtained results thus show that the rectification factor of these diodes can be enhanced, while reducing the temperature difference of their terminals, by increasing not only the emissivity variations between the insulating and metallic phases of ${\mathrm{VO}}_{2}$ films deposited on $r$-sapphire, but also decreasing their emissivity in the metallic phase.