That's called an attic. And yes, attics do help the floors below get less warm.
When you have an attic, you can go further by insulating the roof - this keeps the warm day air out, and during the night you can open windows to let the cool night air in. Historically roof insulation was done with thick layers of thatch, though light-weight synthetic alternatives are more common in modern construction. A well-insulated roof won't let through any appreciable amount of heat.
Then as things get hotter, build the roof taller, allow for natural air flow to dissipate the heat, and finally put the building on stilts so air can flow under it.
Retrofitting existing buildings to have space for good insulation is expensive, especially with the atrocities the US has been building in suburbs for the past 80 years.