First of all, I would recommend growing seedlings at least six to eight inches high before transplanting, and leave a lot of leaves up top after you do. More leaves means faster growth to start with, in my experience.
If it's hot outside, make sure that's not making your growing area inside too hot. That can make it difficult for plants to grow, I've found.
When growing your plants, grow them in at least 18 fl. oz. containers, each. They'll grow bigger faster if they're not in tiny cells.
Phosphorus is supposed to help plants mature more quickly. That seems to hold true, so far. If your plants are maturing faster, you're likely to get fruit faster. Make sure they have enough potassium, calcium and silica (those things will likely make transplanting more successful, if you have adequate levels).
Late in the season, I wouldn't even worry about hardening off, if your area is like mine. In early to mid June on up, hardening off no longer seems to be necessary where I live (western Idaho). In May up to maybe early June, the transplanting is much different, however.
Not too long after planting, I might recommend fertilizing once with an even fertilizer (something like 20-20-20) to get some quick, extra growth in.
Finally, plant early varieties. You might consider those that set well in heat, as well as those that set early. If you're starting late, it'll likely be hotter than usual when they want to bear fruit.
For tomatoes, you might try Early Girl, Glacier, Siberian and Galapagos Island (Solanum cheesmaniae). I believe all of those should do well in heat, and they're all fairly early. Siberian is a cold-tolerant variety, but I've read that cold-tolerant varieties (such as Glacier) often are great for hot areas, too (not all of them, though, perhaps). Cold tolerant tomatoes may also extend your season somewhat.
Pruden's Purple is a nice tomato that seems to mature and get flowers rather quickly, if my one plant is any indicator. However, I'm not sure that it fruits well in the heat.
For hot peppers, you might try Early Jalapeño. It really is early. I'm not sure what else, but I would mostly recommend checking the days to maturity on them.
If you're late planting, I could also recommend looking to your neighbors with large, mature tomato or pepper plants. See if they'll give you a few branches for cuttings. The bigger they are, the better, as long as you know how to root them (whether outdoors or indoors, in soil or water).
Unless you're rooting in water, you'll probably want light levels to be low for the first few days. Using extra potassium sulfate should help success rates if you're rooting in soil. Peppers may be a lot more difficult to root in soil than tomatoes.
Adding a little of an even fertilizer (like 20-20-20) to the water, for cuttings rooted in water may help to keep the plants nourished if the water-rooting is taking more than a few days. A fertilizer that isn't even (like 24-8-16) will often kill your cuttings. Expect it to take up to at least a couple weeks, in water. If the stems have root nodules, it should be much faster.
Tomatoes are a lot easier to root in soil (fresh seed-starting mix) than water, I think.