There are three issues here. Drought is a water issue, and you can manage that. Plain old heat is another. Heat prevents a lot of plants flowering and fruiting. And that's air temperature. There is little you can do about that except provide shade or move them inside to a cooler environment. Shade can help a little, but shaded alone may not do much. For instance, here in Central Texas yesterday afternoon, it was 106 or 107, and it was 104 at my back door in dark shade on a screen porch, way out of the sun. But I think there is a third issue, and that is simply the effect of direct strong sunlight that might normally not be a problem. In fact, a plant might specifically want direct sun. But when you stack that on top of extreme temperature and dry air, it will curl them. It curls me if I stand out there. Shade can help there, too. I'm using 30% shade cloth over some young tomatoes and other things and have them on constant wick watering, and they still suffer some. It's not the sun. It's not the heat (although that's a fruiting issue), and it's not the drought. It's all three combined.

I think all we can do it throw away the sun/shade/partial sun specifications and get everything we can move into somewhere with less brutal conditions. A nice shade tree blocks the sun, and the evaporation from its leaves drops the temperature some. But in the end, it's a fight we will sometimes lose this year.

Purslane often opens late in the morning and closes shop before 5 so if you work you might be missing the blooms. Mine have been in part shade and have bloomed through the Austin TX summer (105-112) watered twice a week in pots. They are in a good succulent soil. It is cooling to 98 now and is still blooming.