Good insulation isn't a problem of the house being too hot. The same mechanics that for it to keep it warm in the winter, works in keeping the heat out in the summer. In the winter do you open your doors and windows? Noooo, you close them.
If you close your doors and windows, then the warm air from outside won't get inside, and the inside will stay cooler. Obviously, you will run into a separate problem of the people inside the closed enclosure generating heat and slowly heating up the space and the matter of oxygen. But that is a different problem to insulation not doing it's job. The insulation is doing its job fine in keeping the heat from the outside getting in mostly, just as well as keeping the heat from the inside going out.
The problem isn't the "thick brick walls" retaining heat, I mean you can't tell me Spain builds houses with thinner bricks...I mean a castle has HUGE bricks, or stones, that is feet deep....they are cooler, so thick thermal mass isn't a problem. In fact, VERY thick thermal mass might be a plus.
A very basic school lessons why houses in the med or hotter climates are cooler, and its not really to do with insulation but more...circulation and physically keeping the heat out.
1 - They paint their buildings white, white reflects heat. It's not that bricks keeps the heat, it's the colour.
2 - They have shutter OUTSIDE the windows, closing the blinds is good but the energy has already gone through the glass and so inside the room is already heating up.
3 - They have high, really high ceilings, and more space for the hot air to rise, so when you stand up, your head isn't near the ceiling. If you go to any warehouse with no air conditioning, it is cooler but if you get on a cherry picker and go up near the ceiling, it is so much warmer.
To keep your house cooler......just tape some cardboard or something on the south-facing (or where the peak sun hits) windows during peak hours, that will lower the temperature by a few degrees. If you can, have cross ventilation. 1 window open is no good, you want windows on 2 sides.