Seriously, John, I have always lamented the fact that most of my English relatives had to visit us in the Summer.
I highly recommend that if you want to visit Texas (though, remember it is so vast that it has major differences in climate zones in its different sections, even on the same day), please come either Autumn or Spring, with Spring and its blanket of wildflowers being the prettiest. March and early April are great. Winter is wonderful along the Texas coast, especially heading SW to South Padre Island, where temperatures are very agreeable.
Autumn is a wonderful time in West Texas, such as a raft trip down the Rio Grande in Big Bend National Park,
or seeing he trees turn colors in Lost Maples State Park.
http://www.tpwd.state.tx.us/spdest/findadest/parks/lost_maples/
If you must visit in Summer, I recommend going straight to New Braunfels, where you can stay perpetually cooled by the spring waters of the Schlitterbahn Resort:

^..^ Julie
