The correct answer is C. Coolly.
The correct spelling of the word is "coolly". The word "coolly" is an adverb that means in a calm and collected manner. It is derived from the adjective "cool", which means not hot.
The word "publiclly" is not a word in the English language. It is a misspelling of the word "publicly". The word "publicly" is an adverb that means in a way that is done or known by the general public. It is derived from the noun "public", which means the people as a whole.
The word "incidentally" is an adverb that means in passing or by the way. It is derived from the noun "incident", which means an event that happens unexpectedly or by chance.
The word "really" is an adverb that means in fact or indeed. It is derived from the adjective "real", which means true or genuine.