considering that these layers are discrete and that the temperature range between them is huge?
Not in the way that you might think.
The concept of temperature is rather different at the Earth's surface vs. what you might measure 250km up (in the thermosphere). A thermometer at the Earth's surface behaves as though it's immersed in a continuous fluid and you'll get a very accurate reading. Keep in mind that "temperature" is a measure of the kinetic energy of the molecules surrounding the instrument.
Take that thermometer 250km up and things are not going to work so well. Molecules at ground level are very much squashed up against each other but art altitude, the spacing might be 5cm apart (for argument's sake). The concept of "temperature" really doesn't mean much in its traditional sense.
