Figure 1. Comparison of two thermometer scales.

Temperature, event measured with different termometer, e.g. $\rm X$ and $\rm Y$, represents the same physical temperature $T$.

Relation between $x$ and $y$ can be formulated as follows.

$$\tag{1} \frac{x - x_L}{x_H - x_L} = \frac{y - y_L}{y_H - y_L}, $$

which is simply ratio of line segments in each temperature scale.

Table 1. Comparation of some common tempature scales.

Table 2. Comparation of other tempature scales.

The names are Celcius, Fahrenheit, Réaumur, Kelvin, Rankine, Delisle, Newton, Rømer.

Except Newton scale, other scales are using freezing and boiling points of water at sea level for $x_L$ and $x_H$.