Answer: First, I'd suggest that you take a look at that soil and see if you might improve it. Lots and lots of organic matter--in the form of compost, aged manure, leaves, grass clippings--can work wonders to improve a heavy soil. (That's the voice of experience!) Organic matter improves heavy soil by increasing drainage and reducing compaction. It will take a few years--but the sooner you get started.....If you're interested in improving your soil, I suggest you have your soil tested first. Soil pH is an important factor in plant growth, and can take some time to adjust if it's way off. Raised beds are another possibility, as is growing in containers.
Though you can't do anything about that hot sun....you can do things to make a successful garden. Start by planting at the right time. Cool weather crops like broccoli and spinach should go out in early spring. Heat-loving crops like tomatoes and peppers should do fine your heat. (Production may drop off during the hottest part of the summer, but pick up once again when the weather cools a bit.) Mulching plants with hay or straw will help insulate the soil from the heat of the sun and conserve moisture. You can even purchase shade cloth if the sun really is too intense for some crops.
Most plants need more sun than can be provided in an indoor environment, unless you have a greenhouse. You can also grow things like cherry tomatoes in hanging baskets, especially if you can hang them on a porch where they'll get at least 6 hours of sun a day. Some plants, notably some herbs, will do fine in a windowsill garden--but most will do better outdoors. You can be creative, such as erecting a simple trellis and planting some vines. Then plant some of the more sensitive plants in the shade cast by the trellis.
I hope this gives you some ideas!
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