Maybe it's just something I don't understand but I would go with Celsius everywhere with converting to Fahrenheit/Kelvin when showing/grabbing temperature to/from user.
However, different coordinate systems that should never be mixed are useful to keep separate. At work we deal with maps and geographic information, so there are always at least three coordinate systems: Screen, projection and geographic coordinates. Having a type system that catches mistakes there would be so much nicer than just always passing P2D around and trying to never mix different ones.