It's been in the 50s in the morning here and I have a similar m.o. where the highest window in the house has a fan that blows out the air all night with the ground floor windows cracked. Then I'm up at 6:00 am and open up the ground floor windows with fans blowing air in. I shut up the house around 8:00 am and today with it 84F at 15:30 it was 67F inside and only got up to 70F by 19:30 when it got to be 70F outside.