After the Kage Summit, if Naruto is cold, it might have a significant impact on his relationships. For example, the other villages might view him as vulnerable now. This could cause some political unrest as some may see it as an opportunity to gain an advantage over Konoha. On a more personal level, Sakura and the others would surely be concerned and do everything they can to nurse him back to health. They might also search for any possible medical or ninja arts solutions to this strange condition.
In the fanfic, Naruto being cold after the Kage Summit could lead to some interesting character developments. His friends might be worried about him and this could strengthen their bonds. Also, it could be a sign of some sort of new power or curse that he got during the Summit, which would then drive the plot forward as they try to figure out what's wrong with him.
It could be due to some sort of chakra imbalance caused by the intense events at the Summit.
In a 'Dark Naruto Kage Summit' fanfiction, it's possible that Dark Naruto is actually a misunderstood figure. He arrives at the summit not to cause destruction but to seek help. His dark transformation might be the result of an experiment gone wrong that he had no control over. The Kages, initially seeing him as a threat, might come to realize his true situation after he reveals his story. This could lead to a different kind of relationship between Naruto (even in his dark state) and the Kages, where they work together to find a solution to his problem.
Well, in the 'Naruto goes to the Kage Summit' fanfiction, Naruto could be in for a wild ride. He might be representing Konoha in some crucial discussions. There could be political intrigue among the Kages, and Naruto, being Naruto, would probably try to cut through all that and promote unity. He may also show off some new jutsu he has learned to gain the respect of the other Kages.
Perhaps in the fanfiction, there are internal power struggles within the villages that are revealed at the Kage Summit. A young ninja from one of the villages might try to influence the decisions of their Kage during the summit. There could also be a cultural exchange aspect, where the Kages learn about each other's villages' traditions and find ways to incorporate beneficial elements into their own villages.
In this fanfiction, Naruto might be pushed to attack the Five Kage Summit due to some misinformation or a threat he perceives to Konoha. Maybe he thinks the Kages are planning something against his village.
A new, young ninja from a minor village could be the main character. They could be trying to make a name for themselves and their village at the Kage Summit. They might get involved in some political intrigue or even a fight between the Kages and prove their worth.
One possible reason could be that something happened during the Kage Summit that made Naruto lose trust in Sakura. Maybe she made a decision or took an action that he didn't agree with. For example, if she sided with someone against Naruto's ideas regarding the situation at the Summit.
Perhaps in the fanfic, a young shinobi manages to infiltrate the Five Kage Summit and has a significant impact on the discussions. This shinobi could bring new ideas or warnings that change the course of the kages' decisions. For example, he might have uncovered a plot by a rogue ninja group to take advantage of the kages being gathered in one place. This would not only create tension between the kages and the external threat but also among the kages themselves as they debate how to handle this unexpected situation.
It could be Naruto himself. Since he has a connection to all the villages in some way, he could play a crucial role in the fanfic, perhaps as a mediator or someone who uncovers a hidden conspiracy during the summit.
She could be confused at first. She might not understand why Naruto is suddenly ignoring her, since they were friends before. So she might try to approach him to ask what's wrong.