CsSnI3 is a promising ecofriendly solution for energy harvesting technologies. It exists at room temperature in either a black perovskite polymorph or a yellow 1D double-chain, which irreversibly deteriorates in the air. In this work, we unveil the relative thermodynamic stability between the two structures with a first-principles sampling of the CsSnI3 finite-temperature phase diagram, discovering how it is driven by anomalously large quantum and anharmonic ionic fluctuations. Thanks to a comprehensive treatment of anharmonicity, the simulations deliver a remarkable agreement with known experimental data for the transition temperatures of the orthorhombic, rhombohedral, and cubic perovskite structures and the thermal expansion coefficient. We disclose how the perovskite polymorphs are the ground state above 270 K and discover an abnormal decrease in heat capacity upon heating in the cubic black perovskite. Our results also significantly downplay the Cs+ rattling modes' contribution to mechanical instability. The remarkable agreement with experiments validates our methodology, which can be systematically applied to all metal halides.