Young massive stars warm up the large amount of gas and dust which condenses in their vicinity, exciting a forest of lines from different molecular species. Their line brightness is a diagnostic tool of the gas physical conditions locally, which we use to set constraints on the environment where massive stars form. We made use of the Atacama Large Millimeter/submillimeter Array at frequencies near 349 GHz, with an angular resolution of $0.1$, to observe the methyl cyanide (CH$_3$CN) emission which arises from the accretion disk of a young massive star. We sample the disk midplane with twelve distinct beams, where we get an independent measure of the gas (and dust) physical conditions. The accretion disk extends above the midplane showing a double-armed spiral morphology projected onto the plane of the sky, which we sample with ten additional beams: along these apparent spiral features, gas undergoes velocity gradients of about $rm 1 km s^{-1}$ per 2000 au. The gas temperature (T) rises symmetrically along each side of the disk, from about 98 K at 3000 au to 289 K at 250 au, following a power law with radius, R$^{-0.43}$. The CH$_3$CN column density (N) increases from $rm 9.2times10^{15} cm^{-2}$ to $rm 8.7times10^{17} cm^{-2}$ at the same radii, following a power law with radius, R$^{-1.8}$. In the framework of a circular gaseous disk observed approximately edge-on, we infer an H$_2$ volume density in excess of $rm 4.8times10^9 cm^{-3}$ at a distance of 250 au from the star. We study the disk stability against fragmentation following the methodology by Kratter et al. (2010), appropriate under rapid accretion, and we show that the disk is marginally prone to fragmentation along its whole extent.
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