Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
Hopeful With Dashes of Darkness
Hopeful
For the most part, hopeful covers the tone for the majority of the book. Manjiro is a pretty positive dude, and since the book is pretty much from his perspective, it makes sense that the tone coincides with his voice and character.
Manjiro tends to speak in positive terms, and the hopefulness of the book often comes through in his dialogue. For instance:
Manjiro pointed to the sky. "Look," he said. Pink light rimmed the eastern horizon and ran down the sea. "Doesn't it look like the light from another world, spilling through a slightly open door?"
[…]
"It's like how I feel about America," Manjiro said. "It's as if I see this little bit of light from an open door. It promises… I don't know what! But I want to go through that door and find out what is there." (2.11.50-52)
How Manjiro feels here is pretty much how the book wants us to feel about Manjiro's prospects in America. There might only be a "little bit of light" at times, but it's light nonetheless.
Then there's the ending, which perfectly captures the overall positive outlook of both Manjiro and the writing:
Within him, Manjiro knew, beat a heart scoured by sand, pounded by waves, burned by sun, and polished by rain and wind. It would always be the simple heart of a fisherman, but perhaps it had also become the mighty heart of a samurai. (5.41.18)
The hope is all in the change from "always" to "perhaps": the "perhaps" carries a pretty big dream on its little alphabetic shoulders—the dream of becoming a samurai. To end on that note is to give us a final sense of how Manjiro views his life even in the most stressful of moments—this is how he feels as he walks to greet an unknown fate.
Dark
As upbeat as Manjiro and the writing tends to be, it's not like there aren't dark episodes in the book. The darkest period, we think, is Manjiro's time on the Franklin, with crazy Captain Davis and the drudgery of an unsuccessful whaling expedition.
Here are Manjiro's inner thoughts, turned all dark and twisted:
He leaned against the mainmast and stared out at the sea, trying to remember what had motivated him before. As if through a gauzy cloth, he remembered that he had desperately wanted to go home. But now he knew that would never happen.
It didn't matter anyway, Manjiro told himself. He wouldn't be accepted at home anymore. Better to live out his days in the middle of his endless, motionless sea. If they didn't make landfall soon, there might not be many of those days left anyway. The little water they had was brackish and foul, the pork moldy, and the biscuits more weevil than bread. Some of the men were suffering from scurvy. (4.29.4-5)
The description he gives of life on board the ship clearly shows a sad state of affairs, but it's the lackadaisical indifference in the words "anyway" and "anymore" that subtly give the whole passage a feeling of futility and hopelessness.