She’s probably thinking that she’s cold and wants to hold my hand
In her head she’s probably like “I’m cold, I hope he holds my hand”.
She’s probably thinking/she’s probably like = 〜思ってるだろう
I hope he holds my hand = 手繋いで欲しいなー
In her head = 彼女の頭の中では
“In her head she’s probably like “____”” は彼女の思ってる事をそのまま言う : “I’m cold...”
“She’s probably thinking ____” は彼女の考えてる事を三人称視点に変えてから言う: “She’s cold...”