I don't think it's a common type. Most Naruto fanfictions tend to build on his existing character traits like his loyalty, his drive to protect his friends and village. A 'naruto has no heart' concept goes against the core of his character that fans usually love, so it's probably not a common genre in the Naruto fanfiction community.
It could imply a fan - created story where Naruto is depicted as lacking emotions or a 'heart' in the sense of being cold or unfeeling. Maybe in this fanfiction, Naruto has gone through some extreme experiences that have numbed his emotions.
His mentor, Kakashi, would also be there to help. Kakashi is very protective of Naruto. He would use his experience and calm demeanor to make sure Naruto gets the best possible care and support during this crisis.
Well, it could be that Hinata says something really cruel to Naruto by mistake. For example, she might tell him that she was only being nice to him all along because she pitied him. Naruto, who has always valued her kindness and what he thought was her love, would be devastated. His whole world view of their relationship would shatter, and his heart would break into pieces.
Well, having a heart disease would likely make Naruto more cautious. He might not be as impulsive in battles or training, as he has to think about his health. This could lead to him developing more strategic thinking rather than relying solely on his brute strength.
Self - reflection is key. If Naruto takes the time to really look at himself and understand why he closed his heart in the first place, he can start to work through those issues. Maybe he realizes that closing his heart is only causing him more pain in the long run and that by being open, he can experience the full range of human emotions again, both the good and the bad.
Sakura would probably be the first one to help. She's a medic - nin, after all. She has the skills to monitor his condition and develop treatment plans.
Perhaps after facing too much betrayal from the village he loves. If the villagers turned on him despite all his efforts to protect them, it might lead him to close his heart in self - defense, not wanting to be hurt again. He's always tried so hard to gain their acceptance and if that was all for naught, it would be a huge blow.
In some fanfictions, Naruto could break Hinata's heart by choosing another girl over her. For example, if he decides to be with Sakura instead. Hinata has always had deep feelings for Naruto, and seeing him with someone else would shatter her heart. It could also be that Naruto ignores Hinata's sacrifices for him and takes her for granted, which slowly breaks her heart as she realizes he doesn't value her as much as she thought.
Another possibility is Gaara before he met Naruto. He had a really tough childhood and was initially very cold - hearted, seeing others as tools or threats. His heart was like a frozen desert, until Naruto's friendship started to thaw it. In this fanfiction, they could explore more of his pre - Naruto state of a frozen heart and how it affected his relationships with others in the shinobi world.