Hello. Would you please tell me what "keep her secret warm" means in the context below?
Does it mean 'not to say her secret to her mother'?
And one more. What does underlined part, not then, mean here?
Thank you.

--------from a children's novel, Honest Truth by Dan Gemeinhart
"Why do you think he ran away? Seems like a terrible thing to do to his parents, after everything they've been through."
Without thinking, Jessie blurted out her answer. Maybe it was because she was tired.
Maybe it was because she didn't want her mom saying bad things about her friend, not then.
Or maybe it was because her heart couldn't hold on to the weight of two terrible secrets.
"Because he's dying," she said, her voice flat.
"What do you mean?" her mom asked through a mouthful of food.
Jessie felt her eyes fill with tears but she blinked them back, pushed them back down inside her to keep her secret warm.
"I mean the cancer's back. They found out last week, after the tests."