I'd have to think more about it, but assuming a mild skewness in the distribution, it shouldn't matter too much. This is not unlike the Mann–Whitney U test wher

I'd have to think more about it, but assuming a mild skewness in the distribution, it shouldn't matter too much. This is not unlike the Mann–Whitney U test where the sign of the difference matters, not the magnitude of the difference. As for the bounds on the distribution, while it's true that there is an absolute minimum temperature, in practice I don't think a temperature anywhere near it has been reached by natural means on the surface of the Earth.