His friends would probably take care of him. Midoriya would be very eager to help, using his kind-hearted nature. He would make sure Todoroki is fed and comfortable.
Todoroki's character development in time travel fanfictions can be quite profound. He may start as a somewhat aloof character, but through time travel, he begins to understand the importance of relationships more deeply. When he travels back and witnesses the relationships he could have had or lost, it makes him cherish the ones he has in his original timeline. His view of heroism also evolves. He realizes that being a hero isn't just about using his powers but also about making the right choices at the right time, which is especially highlighted when he has to make decisions that could change entire timelines.
One common theme is family. Given Todoroki's complex family situation in the original story, many fanfics explore his relationship with his father, mother, and siblings further. Another theme is friendship. They often show how Todoroki forms deeper bonds with his classmates.
One aspect of Todoroki x Midoriya fanfic could be the exploration of their contrasting personalities. Todoroki is often stoic and reserved, while Midoriya is more enthusiastic and emotional. In fanfics, this contrast can lead to interesting character dynamics, such as Todoroki being gradually thawed by Midoriya's warmth and Midoriya learning from Todoroki's calmness. It can also delve into their shared experiences at UA High, like how they support each other during battles or training sessions, which deepens their bond in the fan - created stories.
One great Todoroki and Yaoyorozu fanfiction is 'A New Bond'. It focuses on their teamwork during a difficult mission at school. The story beautifully portrays how their different quirks complement each other.