Bermuda grass (Cynodon dactylon), a warm-season grass, is very heat-tolerant. It doesn't need as much water as other turf grasses once established, but it does need frequent watering while establishing. It sounds like you're doing everything right, but you may not be watering enough, so put your lawn on a regular watering schedule. Around the edges, plant ornamental grasses to help keep this invasive grass in bounds. You can also overseed it with cool-season grasses for winter green.