Lot's of adobe buildings were made by the indigenous people as that's about all they had, mud and clay. Mud and clay are terrible insulators, they retain heat extremely well, which is why they are great for pizza ovens.

In the arid parts of Texas evaporative cooling works really really well but requires a decent supply of water. I've never seen people use solar chimneys in these parts but those older generations could have done it with their technology, as long as they had a source of cool air to pull from.