0 degrees celsius + 0 degrees celsius - 
It looks like it must be using kelvin as its canonical units:  0C + 0C = 273.15 K + 273.15 K = 546.3 K = 273.15 C

The weirdness is that conversions like that don't work for units that have different zero points. Perhaps addition of temperatures isn't really well defined? If 273.15 K + 273.15 K does not equal 0 C + 0 C, despite 273.15 K = 0 C, it's not clear what addition "means" in this context.One restricted form of addition that makes sense (which maybe is what's intended?) is to consider the 1st temperature an actual temperature, and the 2nd temperature a temperature difference in units of degrees-C (or degrees-K, or degrees-F). So e.g.:  "5 C warmer than 30 C"
  = 30 C + 5 C
  = 303.15 K + 5 K
  = 308.15 K
  = 35 C

But then addition isn't commutative. The problem is that "degrees C" is overloaded here, to mean both a position on a scale, and the size of a unit on that scale, with no conventional short way of distinguishing which one you mean (which is one reason Kelvin was invented, since things aren't ambiguous if you put absolute zero at 0 K).