A comprehensive microscopic description of thermally induceddistortions in lead halide perovskites is crucial for their realistic applications, yetstill unclear. Here, we quantify the effects of thermal activation in CsPbBr3nanocrystals across length scales with atomic-level precision, and we provide aframework for the description of phase transitions therein, beyond the simplisticpicture of unit-cell symmetry increase upon heating. The temperature increasesignificantly enhances the short-range structural distortions of the lead halideframework as a consequence of the phonon anharmonicity, which causes the excessfree energy surface to change as a function of temperature. As a result, phasetransitions can be rationalized via the soft-mode model, which also describesdisplacive thermal phase transitions in oxide perovskites. Ourfindings allow toreconcile temperature-dependent modifications of physical properties, such as changesin the optical band gap, that are incompatible with the perovskite time- and space-average structures.