This sensor is simply a temperature dependent resistor (thermistor), so what you have here is a voltage divider.
The 1K resistor is used so that when the thermistor changes the voltage will change. The value is not critical and should be set to roughly the same as the thermistor value at your mid temperature range.
The B constant is a measure of how much the resistance changes with change in temperature and is a characteristic of the individual thermistor type.