I'm especially interested in architectural methods, but others work too. Most of the historical cooling systems that I'm aware of use evaporative cooling, like qanats, salsabils, Roman and Italian houses with inner courtyards with pools or fountains, or just water-soaked reeds or cloth hung in windows. But those work best in dry climates, and I haven't found any reference to similar things in humid areas, but I haven't really been able to find any information on what kinds of things would be used instead.
The closest is one reference to draft-creation in Fujian tǔlóu, but that was a very specific design that didn't spread beyond one small region (and seemed more incidental than intentional, but maybe I'm mistaken).
I'll offer a response based on the archetypical traditional Malay house (also known as the kampung house) which serves as a model for larger gathering spaces. Malay houses were common in villages throughout the Malay archipelago before the colonial period. The solution to humidity was air flow, and a sister problem to humidity was rain and flood. As such, in addition to controlling the heat, Malay houses were also designed to increase air circulation, keep out the rain, and mitigate problems arising from flooding.
In the first section, I will discuss how these goals were achieved through the structure of each house. In the next section, I'll discuss how rain and heat mitigation were supported by the village layout.
Malay houses were generally elongated and interior partitions minimised to promote cross circulation. They were often propped up on stilts to ameliorate the effects of flooding. The additional height also caught wind at a higher velocity and provided visual privacy without the use of walls and hedges which would otherwise obstruct airflow.
The roof was gabled, with a gap in the roof joint to allow for ventilation. Ample eaves provided for effective sun shading and screened the top of the windows from rainwater.
The top of the windows were sometimes open to catch indirect sunlight even when the bottom windows were closed during the rain. Those bottom windows were fitted with slanted wooden panels (think Venetian blinds) to keep the rain out. Sometimes, the panel angle was fixed and the window was opened by swinging outwards. In other designs, the window could not be swung but the angle of the panels could be rotated, such that the window was "fully opened" when the panels were made parallel to the floor.
The materials used were of low thermal capacity, namely wood for most of the structure and attap for the roofing. Brick was almost never used. Attap is also an excellent heat insulator, thus preventing heating even as it is the surface most directly exposed to the sun. Finally, there were no thick walls or pillars to act as heat sinks.
The houses were freestanding and randomly arranged, thus facilitating better air circulation as compared to row houses. In addition, coconut trees and other tall vegetation shaded houses from overhead sunlight, while allowing lateral wind to pass through. (Smaller shrubs did not obstruct airflow into houses propped up by stilts.)
Some of these features were brought into the colonial era. The rainproof ventilating window with slanted wooden panels is the most enduring feature. They are used in colonial bungalows and row shophouses, and also replace glass windows in church belfries and lanterns, thus dissipating hot air as it rises.
I refer mostly to KS Kamal et al; other sources are in the Malay language. However, I've added some observations — especially in the colonial adaptations segment — gathered from walking the ground in my hometown, Singapore. The media linked represent features that are dime a dozen, which I've also observed in my travels in the region.
