I didn't know any of that either. Fair enough, °C it is!
Funny though - every publication I've ever worked on has had the house style rule not to use the degrees symbol. However, this is probably more to do with typesetting conventions than semantics - I guess it's for the same reason that you never use the % symbol either, always spell out "per cent", the reasons for which are no longer relevant but still widely observed.
I still think "degrees" is semantically redundant - Celsius is the name of the scale; a degree is just a unit of division of a scale. We don't talk of length, for example, in terms of "degrees metre".
d.