It is measure in °F (Fahrenheit), °C (Celsius of Centigrade), or K (Kelvin). A change in temperate of 1°C is equal to a change of 1K.
The most common method of measuring temperature is with a thermometer, but can also be measured using thermocouples.
A thermometer has linearity if the substance inside increases by the same volume amount when you give a fixed temperature increase when starting at any temperature.
The sensitivity of a thermometer shows how large a volume increase you will get for each degree of temperature increase. The narrower the thermometer tube, more sensitive is the thermometer.
Thermocouples are an electrical circuit with a voltmeter, a hot junction and a cold junction. Everything that is above absolute zero gives out a very small electrical charge. If you put one of the junctions in something with a known temperature (e.g. melting ice), and the other in what you need to measure, the voltmeter will measure the difference. You can then work out what that equates to in temperature difference if it's calibrated.