US Citizens with a 15 hour layover in Beijing staying at a hotel in Beijing

Hello. Our flight from Bangkok arrives Beijing at 10pm and leaves the next day at 4pm. I believe this still qualifies for a 24 hour transit visa but, since we are leaving the airport, we have to apply for a free temporary stay permit, right? If so, will we be able to do apply for the temporary stay permit that late at night? What information will we need? Thank you!