Time to study the difference between measuring a ratio and measuring a voltage.
The mid-point value of a thermistor and fixed resistor should NOT be measured as a voltage, but as a ratio.
Measuring it as a voltage (Secret voltmeter) is wrong.
If the therrmistor is about the same value as the fixed resistor, then you get the largest ratio variation.
Arduino's 10-bit A/D has 1024 A/D values spread over 5volt, so about 5mV per A/D step.
You should be able to work out how many A/D values you can expect for a certain temp change with the thermistor resistance table.
Leo..