Just a couple thoughts..really hot sun and full sun aren't exactly the same thing. Yes crape myrtles like full sun but they would not thrive out in open desert. They enjoy a 2 to 4 inch layer of mulch over the roots to help keep the roots cool in summer and protected in winter. Just remember to keep the mulch a few inches back from the trunk to prevent rot and discourage pests.
The other, when a tree is described as having a spread of 15 to 20 feet, that means it needs to be roughly 7.5 to 10 feet away from walls other trees etc. in order to have room for roots to spread, limbs to fill out and air to circulate.
