Fervidly means “in a fervid way”: with feeling that is too strong, or at least very hot and intense. Someone who argues fervidly may barely let another person finish a sentence. Someone who writes fervidly about a new cause may sound as if they have been burning with it for years, even if they have not. Same bookish feel as fervid — more at home in a newspaper or a novel than in a text message. If you only need “with strong sincere feeling,” fervently is the safer everyday choice.