When the city of Alexandria dedicated its $14.5 million courthouse this spring, Mayor Charles Beatley looked proudly at the new five-story building and announced: "If its quality is any portent of what the justice system will be like in Alexandria, then it should be the finest. Onward and upward."

More than three months, later, justice in Alexandria seems healthy enough. it's the courthouse that's the problem.

Since its dedication, temperatures inside the federal-style courthouse have fluctuated wildly, with some rooms registering in the frosty 60s, and others in the upper 70s. Workers have been dispatched to cope with leaking air conditioning units, dripping coolant pumps, a malfunctioning security system, keys that don't fit doors, inadequate gauges, and leaks in sewage lines.

For a time, one court clerk welcomed guests, saying, "Come on in to the refrigerator."

"Temperature control? groused court employe Barbara Shamblin yesterday.

"We freeze one minute and roast the next," said Norma Cunningham, another court clerk.

"We have a joke about it," said John Kloch, the city's commonwealth's attorney. "If it's 80 in one room and 60 in the next, we say the temperature's balanced at 70." But Kloch, like most others in the new courthouse, is reluctant to criticize the building, located in the 500 block of King Street. "We have to look at it in terms of what we had in the old City Hall," where the courts used the be located, he said.

Alexandria general services director Paul Schott and courthouse building engineer Rick Dade, say the problems are real, but temporary. As Dade puts it: "The system isn't functioning fully at all yet."

All new buildings, they say, have shakedown periods during which kinks are repaired. But the courthouse has been shaking for three months, and the problems continue.

But the most spectacular problem to date has been the leakage from air conditioning units on the fifth floor. That occurred in June, when water poured into a fourth floor judicial reception room, soaking the beige walls, damaging the drywall, causing wallpaper to peel and soaking the tan carpets, and leaving about a half inch of water on the floor.

The construction management firm for the building estimates the damage from air conditioner leaks at about $1,500, and construction superintendent Joe Kemp says contractors have agreed to pay for damages.

According to Dade, insuring that the various contractors make the needed repairs had been "like a ball game. You run around in a circle until you just say, 'Well, it's easier to do it myself.'"

City officials met with contractors again last week about the problems. Honeywell, whose sophisticated Alpha Delta 1000 Computer is supposed to monitor the system, has been sending out computer people regularly.

City officials are not pleased. Nor are they steaming. "We're excited about it, but we're not going to sue or anything," says Schott. "I'm unhappy about it. I don't like to see the damage. But I believe we'll get it straightened out."

The judges at the courthouse declined to discuss the matter yesterday, though Dade said they are "very mad, very mad.

"But I don't get as many calls from people in the building as I used to," he said. "I guess people understand the situation."