President Carter still has hot water in his bathroom. House Speaker Tip O'Neill still has hot water in his office bathroom. And so does Chief Justice of the United States Warren E. Burger.

But 130,000 federal workers in the Washington area don't -- now that Uncle Sam considers hot water a luxury it can no longer waste on mere bureaucrats.

On last Friday -- Friday the 13th, no less -- the General Services Administration, in the name of saving energy and the taxpayers' dollars, started shutting off the hot water taps in the restrooms and janitors' closets of about 175 buildings the federal government owns or lease here.

But more than a few bureaucrats are in a lather over the new "let-them-wash-their-hands-with-cold-water" policy.

"May the guy who thought this up have a long, hot, dirty summer," said one Department of Energy worker. She found that when the hot water faucet is turned, "nothing happens."

In other buildings, the GSA had made sure that nothing happens by removing the faucet knobs.

"If the faucets were checked once a week and the leaks fixed, that would save just as much," said Commerce Department librarian Lois J. Lanham.

She and her fellow lunch-time joggers at Commerce also found that the hot water had been shut off in the showers in the department's exercise room. But after the workers petitioned, the hot water started flowing again.

The GSA says it has no intention of cutting off the hot water for joggers' and bicyclists' showers in federal buildings. Nor does it intend to close the hot water taps at health facilities, cafeterias or wash-up areas in print shops and motor pools.

Also exempted are the Supreme Court and the Capitol, which are not under GSA control.

"We wouldn't do it anyway," said O'Neill spokesman Gary Hymmel.

"That's an executive order that doesn't effect the Capitol."

At the White House, the hot water tap will be shut off by the end of the week in the four East Wing restrooms, the GSA assured. But the Carter's residential quarters are exempt because it's their home and the West Wing's office restrooms will still have hot water because it is supplied by a solar heating system.

Federal workers outside Washington still have their hot water, too, at least until GSA decides otherwise.

To justify this exercise in governmental efficiency, the GSA has promised, with mathematical pprecision that taxpayers will save the princely sum of $490,233 a year, not to mention 10,683 barrels of No. 6 fuel oil to heat boilers working at 72 percent efficiency.

"The fact is a half million bucks is not a lot of money," says GSA official Rodgers Stewart. "It's not going to solve the energy crisis. Hot water is something we've been used to having but don't need."