The idea is to probe the thermistor voltage divider using the arduino.
You need to know if the positive-side of the thermistor-resistor voltage divider is @ +5V. If so, then you can simply connect the Arduino anaslog input to the junction through a 1K quarter Watt resistor. The input impedance on an Analog pin is well above 100K, typically in the megohms at DC.
If the voltage is greater than +5 Volts, then the simplest way to do what you desire is not
to do it... Seriously, simply use your own thermistor placed adjacent to the one in the thermostat. Use a minimum of 10K with a 10K NTC to avoid self-heating issues!