There are several grasses that tolerate the Texas heat better than most.
Zoysia grass loves the sun and produces a beautiful carpet of grass. The most drought resistant is El Toro, Empire, Jamur and Palisades.
Bermuda grass also loves the sun and there are many varieties that are well suited for drought areas. The best for this area are Celebration and Tifway.
St. Augustine grass likes sun but tolerates the shade. Most popular varieties are Raleigh and DelMar.
Most of us in this area have Bermuda or St. Augustine grass. Even when Bermuda grass turns brown it will usually come back with watering. St. Augustine grass is less tolerant of drought but has few pest problems.