In The Bronze Bow, why do Daniel's cheeks grow hot when Joel informs him of Thacia's message?
Daniel and Thacia slowly develop feelings for each other during the course of the book. They go through a lot together, and Daniel learns a lot about himself by listening to her. In Chapter 20, Joel visits Daniel and Leah to deliver a message; Daniel knows that the rebellion will no longer be led by Rosh, and Joel explains that the rebels will wait for a new leader. While there, Joel tells Daniel that Thacia, who sent a message for Leah, also sent a message for him:
"Leah is very lovely, Daniel. I wish -- Thacia sent you a message too, by the way."
Daniel felt his cheeks grow hot.
"Four days from now is the Day of Atonement. [...] Will you come to town for it?"
(Speare, The Bronze Bow, Google Books)
Daniel's cheeks grow hot because he is reminded of his feelings for Thacia; blushing is usually in response to a deep emotional feeling, whether shame or love. In Daniel's case, it is likely because he misses Thacia and wishes that he could see her, but is afraid of rejection. His feelings grow conflicted later in the conversation as Joel explains that his father wants to arrange a marriage for Thacia; Daniel is internally angry, but the only hint he gives is to tighten his grip on a hammer. The visit leaves Daniel in despair, as he is afraid that the rebellion, and the possibility of a relationship with Thacia, are truly dead.