Diamond in the Rough by Christi Caldwell

Lady Diamond “Glain” Carmichael, paragon of propriety, is horrified when she discovers her headstrong younger sister at the Royal Colonnade Library reading books that would enrage their ducal father. Worse, this disaster-in-the-making has been abetted by an outspoken, opinionated librarian named Mr. Abaddon Grimoire.

Abaddon clawed his way free of a life of poverty and crime thanks to the refuge he found at the Royal Colonnade Library, and he’s determined to help other people find their escapes as well—in the pages of the library’s books! He issues Glain a challenge: Spend a fortnight exploring the volumes on the library’s shelves; if after two weeks, she still wants to prevent her sister from visiting, he won’t interfere.
Abaddon soon realizes that beneath Glain’s icy veneer beats the heart of a loyal, loving, and passionate woman, and Glain comes to see that Abaddon’s devotion to books is a respect for truth and learning. A former guttersnipe and a duke’s daughter aren’t the stuff of matches made in Mayfair, but perhaps happily ever afters aren’t just for fairy tales!