THE EXACT NUM-ber of times the hot line has been used is secret because only the President is authorized to declassify such information. But some instances can be culled from Presidential memoirs. Perhaps the most intense period of use came during the Arab-Israeli Six-Day War in 1967. The very first official message ever transmitted was received in Washington on June 5. Just before 8 A.M., President Johnson recalled in his memoirs, ''The Vantage Point,'' Defense Secretary Robert McNamara called him in his White House bedroom and announced: ''Mr. President, the hot line is up.'' After an Israeli pre-emptive strike against Arab countries, the Soviet leader Alexei Kosygin sent a message saying that his country's forces would stay out of the pending conflict if the United States agreed to do likewise. The President readily agreed.

A few days later, after a United States communications ship was accidentally torpedoed off the Sinai Peninsula, an American carrier task force moved into the area to rescue survivors. Worried that the Soviet Union might misinterpret the Sixth Fleet's maneuvers as intervention, President Johnson sent a message explaining the action. And when it appeared that Israeli troops might advance on Damascus, Johnson assured Kosygin he was pressing the Israelis for a cease-fire, and the Israelis did stop short of the Syrian capital. Secretary McNamara later said that the hot line had proved ''very useful'' in preventing what could have become a direct American-Soviet confrontation.

The hot line was also used in 1971 during the Indo-Pakistani War; during the 1973 Arab-Israeli War, when there was a United States nuclear alert; in 1974, when Turkey invaded Cyprus; in 1979, when the Soviet Union invaded Afghanistan, and several times during the Reagan Administration, with the Russians querying about events in Lebanon and the United States commenting on the situation in Poland.

The hot line is also known to have been used in noncrisis situations. During Salt II negotiations, when President Jimmy Carter's personal letters to General Secretary Brezhnev were repeatedly answered in a style one United States security adviser suggested ''had been written by the 14th sub-secretary of the Foreign Ministry,'' Zbigniew Brzezinski, the national security adviser, recommended that the President send his communications over the hot line. It got Brezhnev's attention, all right, but one White House participant recalls that the Russians, who take use of the hot line very seriously, replied with something akin to: ''Please don't ever do that again!''

THE PRESIDENT MAY have sole discretion over official hot-line communiques, but the MOLINK staff shoulders the prodigious and monotonous responsibility of continually testing the equipment to make certain the lines are in proper working order.