DALLAS—There's no relief in sight for Texans suffering through the worst one-year drought here in at least a century, as deaths mount, crops wilt and drinking-water supplies evaporate in record heat.

The sizzling summer has brought misery across the Southern Plains states, and Texans are bracing for more after enduring the hottest July on record. "It does get hot around here, but what's not normal is how long it's lasted," said Jason Dunn, a meteorologist with the National Weather Service in Fort Worth.

The...