Change the narration: He said, "May I open the window? It's rather hot in here."

Change the narration: He said, "May I open the window? It's rather hot in here."

Explanation
He asked if he might open the window. He mentioned it was rather hot in there.
"May I" in indirect speech changes to "if he might" (polite request).
The second sentence is a separate declarative: "It's" → "it was", and "here" → "there" — both correctly transformed.