Answer by Raakhee V. Menon:
I am not aware if it is explicitly mentioned if they shared any light moments together, but it is quite evident that Lord Krishna did indeed have a sense of deep respect for Karna. More so out of the fact that Krishna was aware of Karna’s actual parentage and also that Karna was nothing but a victim of circumstances.
Karna also didn’t have any open resentment for Krishna. As far as I have understood, they both mutually respected each other. But Karna held back his open affection for Krishna because of the fact that Krishna was very close to his arch nemesis Arjuna. Krishna was un-officially pro-Pandava and Karna knew that if he showed any open displays of affection towards Krishna, it would most likely be misconstrued as him having secretly moved over to the other side by his very insecure mentor. Karna held his allegiance to Duryodhana above everything else in the world. So he would not do anything that would probably upset his ‘friend’.
During the Kurukshetra war, when Krishna meets Karna in private and reveals his true parentage and requests him to join the Pandavas, Karna’s behavior with Krishna is very civil, decent and calm. He didn’t talk to Krishna as if he suspected some foul play on Krishna’s part to try and brainwash him to move over to the enemy side at the eleventh hour. Karna understood Krishna quite well and I personally believe that he knew that Krishna was no mere mortal. He was well-aware of Krishna’s divinity and also knew that if Krishna had indeed chosen that late time to divulge such a big secret to him, giving him an identity he craved for all his life, then there must be some reason behind it.
Bottomline…they weren’t ‘friends’ in the truest sense of the word, but they weren’t foes either. They respected each other and that was just about it.