Corrugated material could provide a white surface to the mid-day sun in the summer and a black surface to the mid-day sun in the winter. Of course you'd need t

Corrugated material could provide a white surface to the mid-day sun in the summer and a black surface to the mid-day sun in the winter. Of course you'd need to take latitude and roof slope into your calculations but I bet if you made the materials in 10-deg increments you could get something "good enough" for most use cases. Or you could just make the material change color based on temperature. This is all known science but getting it cheap enough to be used as roofing is the trick.