I can commiserate with you on the lack of a/c. Most of the time we do fine without it, but there are a handful of days in the summer when it gets miserable. We have predicted highs in the upper 90's today and tomorrow, and those are the days it gets to about 80 inside the house. A few days in a row of overnight lows above 70 and this house can get miserable, especially on the top two floors*. We sometimes have to escape to the bottom floor to stay cool. Blackout/thermal curtains may be your best bet, as they'll help keep thermal heat from coming in during the day.
*The house is a tri-level split that forms a capital T. The top bar of the T is two floors stacked on top of each other like a normal two level house, with the main floor forming the vertical bar of the T set in between the other two floors. So you walk in the front door and there's an entry way with 9 stairs that go up to the four bedrooms upstairs and 7 stairs going down to the 5th bedroom, 3rd bathroom, laundry room and gigantic rec room. The main floor is the living room, kitchen, and both dining rooms. I describe this so the rest makes sense. On these super hot days we do a couple things to stay cool. First, as soon as the outside temperature is equal with the inside temperature on the top floor, we open up all the windows on the top two floors and put a fan in the entry way aimed up the stairs. What this does is create circulation and pushes the hot air up and out of the house. When the temperature outside is finally below the middle floor temp, we put fans in the widows on the middle and top floor to bring the cool air in, paying attention to what doors need to be opened to create the best cross breezes. At first light we (meaning me) get up and slam all the windows shut so the cool air stays in. On really, really hot days we can also draw the curtains to keep thermal heat from getting in, but we don't have thermal curtains, just really heavy regular curtains. If it gets too stuffy in the bird room we just run a regular fan on low to move air around. This generally keeps the house from getting hotter than the upper 70's, even when the outside air temp is over 100. It's a lot of work, but a little planning and those heat waves can be mostly managed. A few days last year we actually broke down and stayed in a hotel, but that was less for the birds than the fact that one of my kids had just had reconstructive surgery on his arm and the cast was getting so wet from sweat that the infection risk was high.