Use some thermodynamics
Using the basic thermodynamics principle of black-bodies, your goal should be to change the emissivity of the surfaces of your house. Each surface has a measure of its ability to both absorb and emit EM radiation (at the temperatures we live at, this radiation is primarily in the Infra-red range).
This heat transfer is radiative, not convective or conductive and it is important to note how it works. While conductive and convection heat transfer always go from hot to cold, a cooler wall can and will emit radiative heat into warmer outdoor air.
Your house will be receiving radiative heat transfer from the sun. This will be much more significant than any heat your house could shed. Therefore, on sun facing sides, you want your house to have a very low emissivity, for example white paint or bare aluminum. This will reduce the amount that the walls and roof of your house heat up in the sun.
However, some sides of your house may never receive direct sunlight. On my house, I have a north-facing wall that never receives direct sunlight. This wall will be heated primarily by convection from the surrounding air. Convection is not affected by emissivity, but the radiation that it loses as IR is. Therefore, on this non-sun-facing wall, I would want a very high emissivity (black paint or glass).
Heat transfer on this wall could (depending on the temperature delta between inside your house and outside) be a net flow out of your house. The same principle could be extended to any other surfaces of your house that do not ever see sunlight. If you have an awning or an overhanging porch, you could install windows in that area to radiate heat away from your house while not absorbing heat into your house.
Incidentally, this principle is more usually used for the opposite purpose, keeping your cold-weather house from leaking too much radiative heat. Window panes, for example, are huge heat emitters, as you can see by looking at anyone's house with an IR camera in the winter. But this very thing you want to avoid in Chicago in the winter can be used to your advantage in Miami in the summer.
Unfortunately, this princple is probably more useful to consider when designing a new structure, but there may be some ways to implement it on the house you have. For example, painting the non-sun-facing side of your house a darker color, or covering sunward-facing windows with a white awning. You'd have to look at the specifics of your house to determine what you can do.