To be frank, it's nigh impossible. You can try to pile on layers of pale foundation, oodles of black eye shadow, and tease your hair to kingdom come. Chances are high it's all just going to fall apart and you're going to look like a hot mess instead of a carefully crafted one.
So what can you do in such high heat and humidity?
Keep it simple, clothing wise, and spiffy up your ensemble with some well chosen accessories:
Here, I chose a simple black lacy tank top and paired it with a dark grey denim mini skirt. I added a pair of striped socks to "goth" it up a bit and some fancy flats with spooky jewelry. A few bracelets help pull it all together.
This look is simple, near effortless, and still conveys a sense of "Hey, I'm alternative!" without looking like you're sweltering to death.
Concerning hair and makeup, simple is also best. You'll want to avoid anything that needs a lot of hairspray or anything dealing with curls. Crimping might do well, since it'll frizz up in high humity, giving a teased look without the hassle.
Updos are great for hot day. If your hair is long enough, pull it up into a simply ponytail and add a hair accessory. Or braid it and wrap it up around your head for a really elegant look.
For makeup, less is more. If you're going to wear foundation I suggest a non-clogging one with SPF or just a simple powder foundation to keep your face from getting shiny. Depending on what type of eyeliner you use, it might just sweat off, so liquid tends to be best. You can find good waterproof eyeliners and mascara at any department store. Summer is the perfect time to stock up on that.
Unless you have a good primer, your eye shadow is likely to crease as well.
I used a primer over my eyelids, then swept a dark purple eye shadow into the crease and blended. Then I put pencil liner on my top lids and smudged it out, then a little on the bottom. I used a simple powder foundation and a pale pink lipstick.
For a 90 degree summer day, not too shabby.