Why does increasing the temperature of a thermistor decrease it's resistance? Surely, upon an increase in temperature, the atoms within the thermistor would vibrate with more energy and therefore more vigorously, hence making the electrons flowing through the electric circuit more likely to collide with one of the atoms, so increasing resistance.
However, the effect of temperature on a thermistor is contrary to this. I can't understand how it can be.
It's analogous to running across a playground: if everyone is still you're less likely to collide with someone, however if everyone is constantly moving from left to right then a collision is more likely.
So why does an increase in temperature decrease the resistance of a thermistor?
 A: Using your playground example....
Imagine if you had to pass a message (electricity) across the playground, when cold you would have to stretch between each fixed person to pass this message. When hot, more people fill the gaps, the message is easier to pass.
Hope this helps :)
A: Thermistor with this particular temperature behavior are commonly semiconductors. In a semi-conductor, there is an energy gap between the (filled) valence and the (empty) conduction band. At zero temperature, no charges are in the conduction band and the resistance should be infinite as the system behaves basically like an insulator.
If you turn on the temperature, some electrons will start to occupy the conduction band and thus contribute to conduction, lowering the resistivity.
A: Olly, the first part of your thinking is correct, as the atoms receive more energy, the electrons do collide more energetically, but they also move "away" from the atom's center.  The further they are from the center, the easier it is for an electric field to "move" them.  This means that for the same effort (voltage), more electrons are moved (larger current). Since R = E/I, the effective resistance decreases as the current increases (for the same voltage).
