[trepanne]

> That said, I can't think of a situation where degrees (of temperature?) would disappear in a mathematical operation.

I regret that the decades that have elapsed since I studied physical chemistry & thermodynamics don’t permit me to make a proper answer, but if you want this to make sense I believe you should look many orders of magnitude smaller- Boltzman’s derivation of the ideal gas law from Newtonian mechanics using statistical methods.

Temperature is basically thermal density; it’s not really a fundamental unit. Chemical engineers use steam tables all the time to convert temperature to heat or other quantities.