Hi Mat,
Use your 100 ohm thermistor in series with a 82 ohm resistor. With your battery across both the current will be high and the thermistor will selfheat. Connect their junction to the base of a transistor wired as an emitter-follower. The LED and its current-limiting resistor connects from the emitter of the transistor to either ground or the positive supply, depending on whether it is an NPN or PNP transistor respectively.
The LED's brightness will change with the thermistor's resistance change, which might not be much.
The LED won't flicker because the thermistor can't change its temp quickly.
What you need is a white noise generator with its output level contolled by the voltage at the junction of the thermistor and its series resistor. You might have to blow on the thermistor for many seconds for it to cool enough to increase the level of white noise driving the LED.
You can amplify the voltage change with an opamp.
Now the circuit eats batteries because of the power required to heat the thermistor, the circuit is getting complicated and it still might have too much delay.