Anything transplanting from a nursery needs a good 'hardening off' period. Normally thought of for seedlings that have been inside, I would bet that you're just sunburning your basils by putting them in full sun so quickly after being in a greenhouse situation. If you have a shade area to set them in starting for just a couple hours a day, extending each day for about 10 days, that might help them acclimate to your sun. After a few days of out in shade, you could try short periods of sun. I'm in Denver, so not as hot, but very intense higher elevation sun.

How big of planters are you using? They're a bit of investment to start with, but I have really good luck with 8 basil plants in an EarthBox planter that has a built in water reservoir. Put it on wheels, and you can roll it around.

I'm wondering about the potting mix you're using. A lot of factors contribute to the success or failure of a container plant.....all the more important because of the hostile conditions.

I'm using an organic potting mix and I'm currently registering a pH in the soil of 7.

I had another question: I keep reading about making sure not to water the leaves. Why is that?

There are a couple things that can happen with watering the leaves, and it certainly doesn't mean that if they get a little drip, then the plant will have problems. First, if watered during the day when it is very sunny, the water can magnify the sun and burn the leaves. Second, if watered at night when it's cool, the water can encourage disease. Also, if you're using a liquid fert, it can burn tender basil leaves too, but basil doesn't really need fert if the soil is fine.

Let me just say off hand that IMO, no plant likes 100, 120F temperatures combined with full sun shine. May be there are some desert plants that might not mind it but even those prefer a little cooler temps.

BACK TO BASIL: it is describe as HEAT LOVING plant but I don't think they will grow in the oven : LOL

So then growing basil in your climate is quite a challenge. I I were to tackle that , I would do the following:

Plant it I a fairly bigger pot , soiless medium,, with extra pearlite. to maintain moisture longer. BIGGER pot for better insulation of the roots and moisture retention.

put the pot on a coaster, so that it can be moved around.

Get a variety that can stand heat better. Just my thinking, a Thai basil should be more heat tolerant than the American Sweet basil.

Water regularly., may be once a day.

fertilize regularly. I would us 1/5th strength ferigation every other day. (fertigation = watering + fertilizing at the same time)

All in all, in hot temps, as you have mentioned, your basil can get by a few hours of morning sun, when it has cooled off a bit during the night.

Thank you so much for all your information.