If we assume that the relationship between resistance and temperature is linear (i.e. we make a firstorder approximation), then we can say that:
Thermistors can be classified into two types depending on the sign of k. If k is positive, the resistance increases with increasing temperature, and the device is called a positive temperature coefficient (PTC) thermistor, or posistor. If k is negative, the resistance decreases with increasing temperature, and the device is called a negative temperature coefficient (NTC) thermistor. Resistors that are not thermistors are designed to have the smallest possible k, so that their resistance remains almost constant over a wide temperature range.

Steinhart Hart equation In practice, the linear approximation (above) works only over a small temperature range. For accurate temperature measurements, the resistance/temperature curve of the device must be described in more detail. The SteinhartHart equation is a widely used thirdorder approximation:
Conduction model Many NTC thermistors are made from a thin coil of semiconducting material such as a sintered metal oxide. They work because raising the temperature of a semiconductor increases the number of electrons able to move about and carry charge  it promotes them into the conducting band. The more charge carriers that are available, the more current a material can conduct. This is described in the formula:
Where i is current, n is the number of charge carriers, A is area of the material, v is voltage and e is the charge on an electron.
The current is measured using an ammeter. Over large changes in temperature, callibration is necessary. However, this is unnecessary if the right semiconductor is used, because over small changes in temperature the resistance of the material is linearly proportional to the temperature. There are many different semiconducting thermistors and their range goes from about 0.01 kelvin to 2000 kelvin (approx. 1700°C)
References I.S. Steinhart & S.R. Hart in "Deep Sea Research" vol. 15 p. 497 (1968)  in which the SteinhartHart equation was first published.
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