I think we are too precious about doing The Right Thing.
Just get a roll of kiddies drawing paper and a roll of washi tape or good masking tape that won't leave marks (that's why I used my washi tape)
Tape that shit up to the *outside* of your windows.
You gotta keep the sun out before it even tries to come in.
If you don't like tape and paper, maybe you have a spare fitted sheet? I've managed to cover 1 set of windows in my kitchen, secured by closing the window on the sheet.