http://www.herbology.com.au/articles/garden/plants-for-a-tropical-herb-garden/
From http://www.helpfulgardener.com/forum/viewtopic.php?f=29&t=56851
imafan26: "Cilantro can be grown only in the cooler months or it will bolt in a month and a half. The tropical and Asian herbs fare better. MInts, basil, oregano, and marjoram are less fussy. Sage, thyme and oregano can be grown as well as stevia. I have better luck with them in pot so I can move them to better positions at different times of the year. Bay leaves actually will grow well in the tropics. Thyme, sage and oregano seem to like a more poorer more alkaline soil that is well drained. Pots are good because you probably have to bring them inside during monsoons. Ginger can be grown in a large pot.
You probably won't be able to grow French tarragon because it will not handle the summer heat, but Mexican tarragon is a direct substitute for the tropics."
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There will be some plants that can take the heat, but won't thrive in full sun. I recommend a covered table. Fasten boards/poles to the sides of the table and tie on some mosquito netting a few feet above. You can use a thicker fabric if it still hurts the plants too much.
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Much of the information I encountered routed me towards gardening in The Philippines, because most gardens' plants that thrive at that temperature come from the East. That might be a good place to start to select plants.
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Good luck.