Thermistors, beings sensors and not loads, never receive anything close to 120 VAC. The control board receives 120 VAC from the wall outlet and converts it into a small DC voltage source, which is then constantly supplied to the thermistor.
How much voltage drops across the thermistor depends on what its current temperature is. This isn’t something that’s easy to calculate, so we rely on charts like the one below. It shows both the resistance and the voltage drop across this particular type of thermistor at various temperatures.