No I think it should not be between quote marks (for sure).
Because the text is telling the reader about what the boy was thinking (not saying).
If the boy said the words, then it would be in quotes.
The boy thought the words, therefore, it is Italics.
Now the question is, should the first word be in capitol (the 'Why')?
Eirman
Why comes after a comma and is in the middle of a sentence.
Therefore, it should not have a capital w.
If one used a semi-colon (;) instead of the comma, a capital may be okay.
Were you aware that there is a "Proofreading" topic here on Experts-Exchange: https://www.experts-exchange.com/topics/proofreading/
Unfortunately it doesn't seem to be frequented as much as it should be and you have more chance of answers in the "Miscellaneous" topic.
Because the text is telling the reader about what the boy was thinking (not saying).
If the boy said the words, then it would be in quotes.
The boy thought the words, therefore, it is Italics.
Now the question is, should the first word be in capitol (the 'Why')?