°C and °F are offset scales, so not every operation on them is meaningful.
A reading on an offset scale is a point; every other quantity is an interval, a displacement. Each rule below falls out of that distinction rather than being special-cased, and each is pinned here because getting one wrong produces a plausible-looking number that is silently wrong.
A point displaced by an interval is a point.
The difference of two points is an interval, not a point.
Conversion is always allowed, in either direction.
K and °R are absolute, so they are ordinary linear quantities and carry none of the restrictions above.
Intervals on an offset scale still combine freely: it is points that are restricted, not the degree itself.
A thermal calculation, to show the rules are not merely academic.