Once the outside temp falls below the inside (late afternoon / early evening) it would help to have window fans blowing outward to vent warm air and draw fresh, cooler air in from another open window or an open door.
As for the blinds/window dilemma of keeping out the sun while admitting a breeze from the window: Depending on time of day and direction the window faces, there should be some optimum setting for the angle of the slats to completely block out direct sun (sunlight cast on the floor will almost disappear) while hopefully remaining horizontal enough not to block window airflow. You might have to tweak it every hour or so until sunset.
If you have sash windows that open vertically plus horizontal blinds, open the window and set the blinds to cover only the closed portion of the window. Again there might be some optimum trade-off between window opening and sun-blocking.