Steep-slope transistors allow to scale down the supply voltage and the energy per computed bit of information as compared to conventional field-effect transistors (FETs), due to their sub-60 mV/decade subthreshold swing at room temperature. Currently pursued approaches to achieve such a subthermionic subthreshold swing consist in alternative carrier injection mechanisms, like quantum mechanical band-to-band tunneling (BTBT) in Tunnel FETs or abrupt phase-change in metal-insulator transition (MIT) devices. The strengths of the BTBT and MIT have been combined in a hybrid device architecture called phase-change tunnel FET (PC-TFET), in which the abrupt MIT in vanadium dioxide (VO₂) lowers the subthreshold swing of strained-silicon nanowire TFETs. In this work, we demonstrate that the principle underlying the low swing in the PC-TFET relates to a sub-unity body factor achieved by an internal differential gate voltage amplification. We study the effect of temperature on the switching ratio and the swing of the PC-TFET, reporting values as low as 4.0 mV/decade at 25 °C, 7.8 mV/decade at 45 °C. We discuss how the unique characteristics of the PC-TFET open new perspectives, beyond FETs and other steep-slope transistors, for low power electronics, analog circuits and neuromorphic computing.