The study focuses on the phase transitions found in hybrid halide perovskites based on 1,6-hexamethylenediamine and lead chloride using X-ray diffraction (XRD), differential scanning calorimetry (DSC), and infrared (IR) spectroscopy methods. It was shown that the low-temperature phase transition is accompanied by a change in the degree of disorder in the inorganic subsystem and the conformation types of the organic cations. The hysteresis of the detected low-temperature phase transition is contingent upon the discrepancy in the response of the “soft” organic and “hard” inorganic subsystems to the energy input/output to the hybrid system as a whole.