HfO2-based ferroelectrics are considered a promising class of materials for logic and memory applications due to their CMOS compatibility and ferroelectric figures of merit. A steep-slope field-effect-transistor (FET) switch is a device for logic applications in which a ferroelectric gate stack exploits a stabilized negative capacitance regime capable to differentially amplify the surface potential in a metal-oxide-semiconductor FET structure, resulting in the improvement of the subthreshold swing and overdrive. In a number of relevant studies of negative capacitance, intrinsic (thermodynamic) switching is assumed, since alternative switching scenarios predict undesirable hysteretic responses in logic devices. However, there is little support from the experimental data showing that the polarization reversal in HfO2-based ferroelectrics is really driven by the intrinsic switching mechanism. In this work, polarization hysteresis loops are measured over wide temperature ranges on polycrystalline Si-doped HfO2 (Si:HfO2) capacitors. The analysis herein, which is based on the classic Landau-Ginzburg-Devonshire theory, yields the temperature-dependent dielectric susceptibility values, which fit the Curie-Weiss law. The extrapolated Curie temperature value is in line with the data obtained for other HfO2-based ferroelectrics using different techniques. The work also illustrates a method to evaluate the ferroelectric equivalent negative capacitance value and range of voltages, aiming at study and optimization of a stabilized negative capacitance FET. This study indicates that the intrinsic switching provides an adequate description of the polarization hysteresis in Si:HfO2 films. This confirms the usability of hafnia-based ferroelectrics for negative capacitance logic devices, and the important role that the intrinsic mechanism plays in the dielectric response of these materials.