Someone who doesn't believe he/she is cool, so overcompensates in ways to prove to others that they are; one who is excessively cute or cheesy in attempting to be cool
The graduate student wanted to fit in with a popular high schooler, so she acted cornycool by bringing jolly ranchers as a gift and giving lots of hugs.
A level of coolness akin to egocentric arrogance. Particularly for celebrities who wear glasses indoors, wear an emotionless facade, or are actively dismissive.