One possible plot could be that Naruto experiences a great betrayal, perhaps by someone he deeply trusted in the village. This could make him lose faith in the bonds he once cherished and become cold towards others. He might start to isolate himself and focus only on his own power, believing that relying on others will only lead to more pain.
One possibility could be a great tragedy that befalls him. For example, if all his friends were brutally killed in front of him by an enemy he couldn't defeat at that time. This might shatter his belief in the goodness of the world and drive him to become cold - blooded in order to seek revenge. He would start to see killing as the only way to get justice.
One possible plot could be that after losing many friends in a major battle, Naruto becomes disillusioned. He might start to see the world as a cruel place where strength is the only thing that matters. So he shuts off his emotions to avoid further pain, and becomes cold - hearted towards his former allies and enemies alike.
If Naruto becomes cold - hearted, his relationships with the villagers would change drastically. The villagers, who once saw him as a hero, would now be faced with a cold and unapproachable Naruto. Children who used to look up to him would be scared. His friends from the Akatsuki days, like Nagato, might even see this new Naruto as a threat. Overall, his relationships would go from being warm and friendly to cold and distant, filled with suspicion and unease.
Well, at first, people around him would be very confused and try to reach out. But Naruto would just push them away. Then, his former friends might start to get frustrated with his coldness. Some might even turn against him thinking he has changed for the worse.
One possible plot could be that Naruto has faced so many betrayals. Maybe his friends turn on him due to some false accusations. This shatters his warm - hearted nature, and he becomes cold as a defense mechanism. He starts to isolate himself and no longer trusts easily.
His friends in Team 7, Kakashi included, would be deeply concerned. They would try to figure out what made Naruto change. However, Naruto's coldness would make communication difficult. He might distance himself from them, seeing their attempts as interference. His relationships with the villagers would also change. People who once looked up to him might now be afraid of him, as his cold demeanor is a far cry from the hero they knew.
In the fanfiction, the plot could revolve around Naruto being influenced by a powerful and evil organization. They manipulate him into believing that the only way to bring peace is through force and killing. As he becomes a cold - blooded killer, we would see him going against his former comrades. There would be intense battles where Naruto uses his new - found ruthless tactics. His character arc would be a dark descent from a hopeful hero to a feared killer.
One possibility could be that Naruto is drawn to boxing because of its physicality and the determination it requires. He might see it as a new way to test his strength and endurance outside of ninja battles. Maybe he starts training with a local boxing coach who sees his potential and helps him develop his skills.
It could be an evil wizard. There are many powerful and malevolent wizards in the Fairy Tail universe who might target Natsu for some reason and use dark magic to make him cold.