We tend to keep the blackout blind in DS's room closed during the day but the windows open as the sun is on his room for the hottest time of the day. As the sun moves around we then do the same for DD's room.
It stops the rooms from heating up too much yet still allows air flow through the room and house.
Can you close the window when you go to bed? I usually put DD2 (16 months) in just a vest, with the window open, and then close the window when I go up. If it's very hot, we use a fan, again, turn it off when I go to bed.
We have a portable airconditioner. We put it in my older boy's bedroom for an hour or so before they go to bed to cool it down. Then we take it out and put it in our bedroom where the baby sleeps. We also have fans on in both rooms overnight.