He would probably be more distant. For example, he might not join in on the guild's boisterous celebrations. Instead, he would sit in a corner, observing. When his guildmates try to engage him, he gives short, curt responses.
Natsu with a cold personality might be more of a lone wolf. He could avoid team - up missions and only go on solo ones. If he has to interact with his guildmates, he would be more business - like. He would not show the usual camaraderie and might even seem impatient with their more light - hearted antics. He would no longer be the center of the guild's fun - loving chaos but rather an outsider within the guild.
Well, at first, his guildmates would be very confused and perhaps a bit hurt by his coldness. He would not participate in the friendly banter like before. Gray might try to pick a fight with him to get some reaction, but Natsu would just walk away. Erza might try to talk some sense into him, but he would be dismissive. Over time, some guildmates might give up on trying to reach him, while others, like Lucy, might be more persistent and try to find out what's really wrong with him.
Perhaps in the fanfiction, a cold - personality Natsu has lost his memories of his former self. He becomes a loner who is feared by many because of his icy demeanor. The story could then revolve around a character trying to help him regain his memories and bring back his old self. For example, Lucy could find an ancient spell that might restore his memories but has to go through many trials to use it.
If we consider the magical aspects of their powers, a Dragneel's power might be more raw and instinctive, while a Fullbuster's power could be more controlled. When they interact, the Dragneel's power could add intensity to the Fullbuster's ice spells, making them more powerful and long - lasting. Or the Fullbuster could use his ice to contain and direct the Dragneel's fire, creating a more focused and destructive force.
Natsu is very impulsive. This might make him overprotective of his daughter in the fanfiction. He might jump into action at the slightest sign of danger to her. For example, if she's in a simple sparring match in the guild, he might be tempted to interfere if he thinks she's in real danger.
One way would be through a magical portal. Maybe some dark magic in the 'Fairy Tail' world accidentally creates a portal that sucks Sakura into it. Once in the Fairy Tail world, she has to adapt quickly. Natsu could be the first to find her. He's initially confused by her ninja abilities but soon realizes they can be useful. They then work together to close the portal that's causing chaos in both worlds. In this way, the two worlds start to blend as they exchange knowledge and skills.
He might be more in tune with nature. Since dragons are often associated with nature, Natsu could have a deeper respect and understanding of the natural world around him, showing more kindness to animals and plants.
Well, I'm not sure how widespread it is, but it's possible to find such fanfiction. Writers often like to mash - up different universes to create something new. In a 'Harry Potter is Natsu Dragneel' fanfic, you might expect to see Harry with Natsu's determination and love for his friends translated into the context of the wizarding world. Maybe he'd be more brash and use his 'fire - like' magic in a more aggressive way like Natsu does.
A common plotline is the rescue mission. His friends from Fairy Tail band together to find and save him. Another is Natsu trying to break free on his own. He might use his fire magic in creative ways to escape his bonds.
His impulsiveness might decrease. As an old man, Natsu would have more life experiences. He might think twice before jumping into a fight. For example, he would consider the consequences for his friends and the guild.
Edward's determined personality would likely make him eager to learn about the German environment. He wouldn't be afraid to ask questions and explore. His hot - tempered side might get him into some minor conflicts at first, especially if he encounters strict German traditions or rules that he doesn't understand immediately.
It could be another male character who is also interested in the same person as Natsu. This would create a love triangle. He might be from a different guild or have a different type of magic, and the competition between him and Natsu for the girl's love would be a major part of the story.