Update, 11:48 a.m.
The number of outages in downtown Galveston has been reduced to 20 customers, according to Centerpoint Energy.
Some 400 homes and businesses were without power on Monday morning, according to Centerpoint Energy.
The outage began about 10:15 a.m. and initially affected about 500 power customers north of Broadway between 25th Street and the University of Texas Medical Branch.
At 11:30 a.m., the number of customers without power had been reduced to about 400, according to a Centerpoint Energy spokeswoman.
The company had initially estimated that all power would be restored by 11 a.m., but later said there was no exact estimate for customers without power after that time.
The outage affected some downtown businesses including the box office at The Grand 1894 Opera House and restaurants along Postoffice Street.
Temperatures in Galveston were expected to reach the low 90s on Monday, though forecasted humidity will make it fell hotter. The city is under a heat advisory, according to the National Weather Service.
Galveston city facilities, including city hall, the Rosenberg Library and the city's recreation centers, all have power and air conditioning, officials said.