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Theoretically, the Celsius and Fahrenheit (and other) temperature scales are linear scales based on the volume of an ideal gas as it changes with temperature. And the size of each degree in the Celsius scale is based on 0 degrees for freezing water and 100 degrees for boiling water, at standard pressure. The Fahrenheit scale is now based on 32 degrees for freezing and 212 degrees for boiling. Since both scales are linear, there are simple conversion formulas (See Fahrenheit To Celsius). Most gasses are nearly ideal gasses. And ideal gas is a theoretically perfect substance that compresses like a gas, right down to nothing at absolute zero.
For some purposes, the above describes the real situation. But, for most purposes, the situation is incredibly more complicated. The General Conference of Weights and Measures, an international organization, defines the International Practical Temperature Scale (essentially the Kelvin scale) which goes from 0K (zero kelvin, where kelvin (not degree) is the unit) at absolute zero and has a unit that is 1/273.16 of the temperature difference between absolute zero and the triple point of water (temperature and pressure where water exists as gas, liquid, and solid simultaneously). This scale is theoretically linear, except that they apparently choose to measure different phenomena (like the freezing point of gold) at eleven different temperatures. Then temperatures are interpolated between these eleven points. They adjust this scale every twenty years. The Celsius and Fahrenheit scales are deduced from this scale. And so, they not really linear; but they are really close to being linear. And 0 degrees Celsius, (as well as 32 degrees Fahrenheit) is not really the freezing point of water anymore, but it is really close. Most encyclopedias do not even mention most of this.
Originally (1742), Celsius' scale was reversed, with freezing being 100 degrees and boiling being 0 degrees. I have two thermometers that differ by two or three degrees, and both are guaranteed accurate. The guarantee did not mention how accurate they are. Maybe I need a third thermometer to determine which one is inaccurate.