Hi,
If you are unwilling to use the LM35 in order to avoid ADC, then using a thermistor will not help, as there you would also need the ADC to measure the change in voltage across it due to change in resistance due to change in temperature. If you are don't want to use ADC, you can use something that uses I2C/TWI (TC74) or SPI (TC72) or one-wire(DS18S20) protocol.
But if you want to use thermistor, this is how you could do it. Set it up with another resistor such that the resistors form a resistor divider network the output value of which will change proportionally with change of temperature as this causes resistance to change. In this case you need to know the resistance of the thermistor and the voltage drop across it at a specific temperature. Then measure this voltage.
Hope it helped.
Tahmid.