What is the best way to transplant wandering jew and some other plants during very hot summer?

Question:I am tearing down a section of my house and remodeling and I will need to transplant a lot of dark purple wandering jew, gaillardria and mexican sunflowers from right next to the house. I want to keep them healthy so they can be replanted after the building is done. These are very extablished plants planted by the former owner over the last 50 years. They are really deeply colored and I don't want to loose them.

It is summer in Phoenix, so I want to do this without shocking them.

Answers:
wandering jew...make cuttings from existing plant, and just plant it - water it...this plant takes off like a weed...you don't need to root or anything.
the others, you will need to cut and place in water to root - then plant.

make sure you water them every day in the heat and mist them also.
i live in san diego...not as hot as you, but we have been having heat lately...i water mine every day and mist a few times a day.

good luck :)