Main energy gain happens because of the radiation. I think that the best combination is high thermal mass structure followed by the insulation inside. This way

Main energy gain happens because of the radiation. I think that the best combination is high thermal mass structure followed by the insulation inside. This way the heat is not easily transmitted to the inside and the thermal mass can cool off to the outside during the night. Of course when the heat finally does get inside then it is trapped because the house will act like a thermos and only way of cooling would be the by circulation of cold air. Problem of windows can be solved by outside blinds (or shutters but blinds are better) and IR reflective coating.