Nice to see that one mentioned
If you want to use DS18B20 the resolution and time are strongly coupled. More resolution means more time. In my experience it is not fast enough for your requirements (although I never tried such differences)
Check - http://www.temperatures.com/
- for alternative solution.
There are however other means to measure temperature of the air. The speed of sound in hot air is different from cold air. If you take an ultrasound distance sensor and let it monitor a fixed distance to a "wall" e.g. 100 cm and the airflow is between the sensor and the wall, the distance reading changes predictably and superfast.
Check my post in this thread - http://arduino.cc/forum/index.php/topic,65205.0.html
- (11) for a theoretical backgrounder
float SpeedOfSound = 331.45 * sqrt(1 + T/273); // T in Kelvin
distance = SOS * time = 331.45 * sqrt(1 + T/273) * time;
As you have a distance you need to invert this formula to get the temperature (left as homework