For dry, you see a fair number of examples in the US southwest. One of the things you do is take advantage of the fact that there are big temperature swings between daytime and nighttime. You can also use cooling towers. You get some idea from the design of the Zion Visitor's Center. [1] It's not hot-hot there (it's high but gives you some idea).
Wet hot is a lot harder. Utilize shade where you can. Lots of cross-ventilation. Basically very open buildings (subject to how big a problem biting insects are of course--though you can use screens in that case).
Yeah, I visited the Andrew Jackson home and there were a bunch of corridors basically designed to convey wind (though ironically they keep them shut now because the moisture would damage the home)
Swamp coolers are incredibly useful for efficiently keeping cool in 100+ degree days, but are only usable in "dry heat".
Everywhere south of about Pennsylvania, kissing bugs -- carriers for deadly Chagas disease -- become a problem. So even with screens, you're going to want a well-sealed house.
More emphasis on airflow, more earthworks, more trees, and more passive solar design. That means fewer south facing windows, open features like patios, less bare lawns, building into berms, and various forms of sunshading.
I live in such a climate, and a pergola I built specifically to shade the west-facing sliding glass door has probably made a 10 degree difference in the temperature of that room. Great example of where A/C previously let the architect be lazy.
Whole house fans for cooling at night, insulation & air sealing up the wazoo for staying cool during the day. More focus on radiation-blocking windows.
Look up traditional persian architecture, at least for dry heat.
Thick walls, emphasis on airflow (windcatcher structures and solar chimneys) and interesting canals engineering (underground canals — qanat — used as heat exchangers to cool down surface air before drawing it back up through dwellings).
Engineering around shade also becomes very important.
Plenty of houses have been built across the southern USA before AC was common. When I lived in Tennessee, my house had a big shaded porch in front, plenty of shade trees, and (best of all) a huge 3 ft diameter whole-house fan in the hallway ceiling that kept a nice breeze coming in through the windows.
It was still uncomfortably warm on hot (and humid) summer days, but tolerable.
It's quite common to not have air-conditioning in Sydney despite the temperature reaching over 40c in summer. The only really noticeable thing for me compared to Northern European housing is double glazing doesn't seem to be as prevalent.
