A thermistor is a piece of semiconductor. A semiconductor has very interesting properties. At very low temperatures, a semiconductor is basically an insulator because it does not have any mobile charge carriers to carry any current. At higher temperatures, electrons are “shaken loose” from the atoms and become mobile. The higher the temperature, the higher the charge carrier concentrations (more charge carriers per unit volume). This results in a decrease in the resistivity of a semiconductor, and thus a decrease in the resistance of a thermistor.
As the I-V graph reveals, a thermistor has a different constant resistance at different temperatures. The higher the temperature, the lower the resistance.
Thermistors are usually operated at low power. So it usually does not heat itself up, unlike the filament. In fact, thermistors are often used as temperature sensors. So a thermistor’s temperature is usually decided by the ambient temperature (or the temperature it is supposed to be sensing). But if for some reason, extremely large voltages are applied across a thermistor, so much so that it heats itself up, then it’s possible that its I-V graph will steepen to correspond to the decreasing resistance.