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13a It's getting warmer -1°C each century principally apparently. The only thing that will fit is ice cap. Why does 1°C equal ic, please?
e and c are the principal letters of each and century but why is ap short for apparently, please?

In my Chambers Crossword Dictionary ap is given as an acceptable abbreviation for apparently.

Ignore the degree sign.
ap is abbrev. for apparently (Chambers confirms)

'ap' is given by Chambers as an abbreviation for 'apparently' (and 'apparent'), so it's legit, although I'm surprised to see it in a DM crossword, where one expects a rather less 'rich' (ie obscure!) abbreviation palette to be used.

'1' and 'I' are treated as interchangeable in puzzles ('I' being the equivalent Roman numeral to the Arabic '1'), but I cannot justify the replacement of '°C' with 'C'.

I thought this a very iffy clue too.