A fierce but brief thunderstorm, fueled by record-setting heat, lashed the Washington metropolitan area yesterday, cutting off electricity to thousands of homes and critically injuring a woman in a car struck by a falling tree.

Bringing winds that gusted up to 55 miles an hour at Dulles Airport and up to 45 miles an hour at National Airport, the storm swept across the area about 4 p.m. on the first full day of summer and the sixth day in the last nine on which the mercury bubbled into the 90s.

In an unusual twist, a thunderstorm that soaked much of the Washington area three days ago was blamed for a minor drought that parched Fort Belvoir yesterday, curtailing many activities and causing many civilian employes to be sent home.

An Army spokesman explained that on Saturday lightning damaged a key valve mechanism in the base's water supply system, causing a plunge in pressure, the severity of which did not become apparent until yesterday. Employes were sent home to redue demands on the system so repairs could be made, the spokesman said.

Meanwhile, yesterday's thunderstorm knocked out power for periods of less than an hour to about 10,000 Arlington, Vienna and Falls Church customers of the District of Columbia lost power.

In Rock Creek Park, a tree toppled onto a car at Beach Drive and Park Road, pinning a woman inside. The victim, identified as Theresa Van Houten, 42, of Kensington, was flown by U.S. Park Police helicopter to the Washington Hospital Center where she was listed in critical but stable condition with spinal injuries.

The temperature at National Airport reached 97 degrees, matching the year's highest and eclipsing by one degree the old record for the date, set in 1873.

Yesterday's heat, humidity and atmospheric turbulence are expected to give way today to cool, dry and more pleasant weather, with a high of about 84 to 88 degrees.