Shutting the windows only works if no direct sunlight never hits the windows. If it does, the temperature will increase faster inside the house than it would with the windows open, especially if the floors are concrete. It also depends on the thermal mass of your insulation. The higher the thermal mass, the slower the walls are to change temperature. This is usually a good thing where temperatures change above and below a desirable temperature from day to night. It causes the temperature to somewhat regulate inside. That's why underground is at a relatively constant temperature.