The hysteresis might have been set to take into account the nature of the cooling radiator in much the same way the mechanics of the bimetal sensor set the hysteresis.
My point is that the hysteresis was in part negated by the position of the sensor, which as you say is next to the heat exchanger.
Sorry, but hysteresis is hysteresis, whether through a mechanical switch or electronic means. I accept if you have access to the code then obviously you can make an equivalent of an 'accelerator heater' and save a component.