(covers information from several alternate timelines)
In the alternate reality, the Federation had already encountered the K'normians by 2259. Kirk confiscated a K'normian trading ship during the Mudd Incident a month before using it to infiltrate Qo'noS. (Star Trek Into Darkness)
In an article appearing in the January 2002 edition of Star Trek: The Magazine Volume 2, Issue 9, entitled "Who is that Alien?", the following information about the K'normians, as taken from Fletcher's original background notes, added:
"The K'normians were a mostly normal humanoid race, though they did have large foreheads not unlike the Klingons, which Fred Phillips also redesigned for The Motion Picture. The K'normians' large brains provided an eighth sense that gave them a superior appreciation of time and space."
K'normia (Psi Tauri) was the name of a star in the Alpha Quadrant. The primary was a Class F star. Magnitude of this star was +5, which was the same brightness as Sol. K'normia was the name of a planet in the system. too, and had, by 2378, become a member of the Federation. (Star Trek: Star Charts, United Federation of Planets I & III)
Kirk thought he and his men could pose as K'normian arms dealers without plastic surgery, suggesting that sometimes they looked more human or that they sometimes employed Humans.