Could you have a quartic or square degree Celsius or other degree on a temperature scale raised to any power?
The units of the Stefan-Boltzmann constant are watts per square meter per quartic kelvin, so it is possible with kelvins. But a kelvin is not a type of degree, although it is a unit of temperature, and is in fact the SI unit of temperature.
Please note that I'm not sure about any of this, your feedback in the comments would be welcome. I'm not sure "per quartic kelvin" is optimal, though it is sometimes used; perhaps "per kelvin to the power four" is better. I know that nomenclature can be a controversial and emotive subject, even in science.
Searching the Internet turned up no trace of a square degree of temperature, and Wikipedia has no disambiguation page for "square degree" and says, "A square degree (deg2) is a non-SI unit measure of solid angle. Other denotations include sq. deg. and (°)2. Just as degrees are used to measure parts of a circle, square degrees are used to measure parts of a sphere."
So it's possible to write it, but it only means square degree of angle, according to Wikipedia. https://en.wikipedia.org/wiki/Square_degree
So my question is: could you have a quartic or square degree Celsius or other degree on a temperature scale raised to any power?