Let me give you an example and then tell me if you need more help.
Say we had a 12 V battery, Thermistor and 100 ohm resistor connected in series.
Now let us say at 20 degrees, the thermistor has a resistance of 100 ohm and that some fan, connected to just the resistor, needs 4 V to turn on.
Well, they both have the same resistance, hence voltage drop for both would be 6V each.
However, let us say that the temperature increased to 80 degrees, and the resistance of the thermistor increases to 400 ohm.
What would happen now?
Well, Due to the thermistor having a higher resistance, it will have a higher voltage drop, which would be 9.6 V.
Now the resistors voltage drop would be 2.4 V. Which is actually less than needed to turn on the fan.
Well, We can increase the resistance of the resistor and this in turn will allow it to have a higher voltage drop.
Does that help?