1) When you read most gardening books and they talk about summer "hot" conditions, they have no idea what hot is or what summer is. Most of the gardening books are written by people up north (no offense northerners, I have enjoyed the books and the advice, we just need to make adjustments) and when they talk about summer heat, they mean mid to upper 80's with maybe a few 90's mixed in. Two summers ago we had two weeks straight over 100 degrees and most of July, August and September saw 90's. So what can we do in HOT areas? Build up your organic level in the soils like crazy (more on this later) and try to never have bare dirt exposed to the elements - green manures as catch crops, organic mulches, or whatever else you can do to preserve moisture and cool the soil.
2) Organic soil content- compost, green manure cover cropping, organic mulching; do it all!. When those books from up north, tell you that you will need 2-3 inches of compost per year, try to double that in two applications. One for your early spring planting and another in mid to late summer when that one is mostly gone. In our heat and long season we can use up a lot of compost. By helping to hold on to ground water, lots of organic matter will help your veggie plants survive (they will not thrive, but survive) the worst part of the summer. Green manures as catch crops planted in early summer where the early cool crops (lettuce, spinach, etc.) have bolted will help the soil organisms survive the worst of the summer. You can plant more of the cool season stuff for the fall (and some may last all winter) in September and October.

The heat of the summer is the bad news. The good news is that we have an incredibly long growing season (officially 214 days for me, but this can be extended). With careful choices of veggies I have had something in the garden that I can harvest fresh through the entire winter most years that I have been gardening here (which has not been that many, but still...). With a little more global warming, I may be able to have fresh tomatoes in January, LOL.
Speaking of those maters, they will take a break in the heat of the summer. Keep them alive. They will pick back up when the heat dies down a bit and you will get a few more fresh ones before the frost kills them in the fall. With our fall cooling routine it is not unusual (with the judicious use of plastic and light bulbs during the cold snaps) to get my tomatoes to last into mid November some years.
For cool season crops, or root veggies you have two seasons, before the hot and after the hot. I have had carrots in the ground all winter, spinach and lettuce all winter, beets and chard all winter. This fall I will be trying brussels sprouts for the first time, but I fully expect them to last all winter as well.

Keep your roots as cool as possible and enjoy the long season and mild winters in the garden.

Steve

Clearly you can garden organically. Have you read all the FAQs on this forum? There is a wealth of info there. I wrote the one on Organic Lawn Care so pay particular attention to the sage wisdom in that one ;-)

I assume you are on sand. The keys to hassle free organic gardening are as stated here by Malcolm Beck.

SEVEN RULES to farm and garden by

After a life time of studying nature, and finally learning to farm and garden in tune with the natural laws, I have come to the conclusion that there are rules to follow that will make our plants grow abundantly, free of troublesome insects and disease, be more nutritious and even taste better.

1. ALWAYS USE THE BEST ADAPTED VARIETIES FOR EACH ENVIRONMENT.
   
2. PLANT IN THE PREFERRED SEASON
   
3. BALANCE THE MINERAL CONTENT OF THE SOIL
   
4. BUILD AND MAINTAIN THE ORGANIC CONTENT (HUMUS) OF THE SOIL.
   
5. DO NOTHING TO HARM THE BENEFICIAL SOIL LIFE.
   
6. CONSIDER TROUBLESOME INSECTS AND DISEASES AS SYMPTOMS OF ONE OF THE ABOVE RULES BEING VIOLATED.
   
7. HAVE PATIENCE. MOTHER NATURE GIVES BIRTH, BUT FATHER TIME CONTROLS THE CYCLES.
   

Malcolm Beck

Your job is to get organic material ONTO your sand and let the microbes in the sand do their jobs. Roots are the very best organic material so always, Always, ALWAYS keep stuff growing to get more roots INTO the soil. When the roots die, they become the organic matter in your soil. Grow grass or weeds if nothing else. Clover makes an excellent 'cover crop' when nothing else is in season. Because the roots grew there naturally, they belong there and are meant to decay there. Tilling surface material into the soil to increase the organic matter below the surface is unnatural. It will happen naturally if you let it.

When you are finished with a crop, don't plow or till it (that would violate rule number 5). Instead mow it down and leave it as a mulch. That leaves the roots intact and protects the soil from the sun.

And don't forget to read my FAQ. I get paid by the viewing (not really). Actually that FAQ is ancient. I'm rewriting it for another forum and will publish soon. I had hoped to have it by now but I don't. It will have more info but will not be all one long essay. And it is still lawn oriented.

I've just finished planting a bunch of fruit trees in central fla; I'll soon find out in I've made the right plant choices. The soil here is bottomless sand with a thin layer of organic matter on top composed of the breaking down of bahia pasture. Ultimately I want to find a team of garden plants that will thrive in soil made from a steady rotation of smothered grass-plots. So far I know that sweet potato and seminole pumpkin are first-string on that team. Dent corn may be as well. Certain greens at certain times of year.