I will arrive Heathrow T3 at 6:10pm. I will depart from Heathrow T5 the next day at 6:30am for Madrid. I plan on staying at one of the airport hotels (probably the Sofitel at T5 since it is directly connected to the terminal), as there is nowhere to sleep in at the airport terminal.
Will I need to go through Immigration and Passport Control to transfer terminals and stay in the airport hotel?
Will I need a transit visa?