A fresh breeze will blow through the stuffy Pentagon come Jan. 12, when Paul Thayer reports for duty as deputy secretary of defense.

The former chief executive officer of the sprawling LTV Corp. is a free-swinging pilot who is bound to provide a sharp contrast to his boss, Defense Secretary Caspar W. Weinberger, and most of the other denizens of the Pentagon's third floor E Ring.

"If you substituted Paul Thayer for Chuck Yeager in the book 'The Right Stuff,' you'd capture the spirit of the man," said one of his associates.

By contrast, one of Weinberger's associates said of the controlled but unfailingly pleasant lawyer-defense secretary: "Cap was born in a suit."

The current deputy defense secretary, Frank C. Carlucci, is the archetypical Washington back-room operator, with a passion for secrecy and distrust of the press.

He will become a fellow at the Hudson Institute after he leaves the Pentagon this week.

Thayer is a man who at 63:

* Roars around the Colorado mountains on one of the two motorcycles he owns.

* Eschews the LTV limousine, driving himself to work in a red Mercedes-Benz coupe instead.

* Takes the controls of any airplane within reach, including the company jet, which he delights in snapping into such a fast roll that drinks don't even slide off the trays of his startled guests in the back of the plane.

* Shoots close to par in golf and once won a lot of money at Burning Tree Country Club by playing the first hole blindfolded.

* Stunned fellow defense contractors at a big gathering in Wyoming this year by climbing into a Corsair propeller plane of World War II vintage and putting on a thrilling air show.

* Calls almost everyone by his first name, loves to party and play poker and generally enjoy life in the mold of a storybook fighter pilot, which he was.

Starting in 1942, Thayer flew Navy fighter planes over Africa and off carrier planes in the Pacific, shooting down six enemy fighters, enough to become an ace.

After the war, he became a celebrated test pilot, first for Chance Vought Aircraft, then for the Northrop Corp., and then back to Vought, where he started a fast climb up its executive ladder.

He became president of LTV Aerospace Corp. in 1965, chief executive officer of the LTV Corp in 1970, a job he relinquished by choice on Dec. 1 to become chairman of the board. He is currently president of the Chamber of Commerce of the United States, a platform he has used to urge an all-out effort to cut the federal deficit, including cuts in the defense budget that Weinberger, his new boss, guards so zealously.

Although Thayer knew some Reagan administration officials, particularly James A. Baker III, he was not a close friend of either the president or Weinberger. In fact, he originally backed the presidential candidacy of John B. Connally, who hails from LTV's home ground of Texas.

Thayer's name kept coming up as the White House searched for a Carlucci replacement who, it was hoped, would know the technical side of the biggest and most complicated military establishment in the world.

Thayer's managerial style is to demand pithy summations of a problem, make a decision more by intuition than by reading thick reports, and then announce it quickly and move on to the next project.

A longtime aide predicted that Thayer will leave his Pentagon office at a civilized hour and depart without a briefcase full of papers.

He arrives at a time when the administration is in dire need of someone to shore up its credibility on its defense program, with the MX missile the leading case in point. Thayer told his many close friends on the Senate Armed Services Committee that he knows how to knock heads to cut waste out of military programs and will wade into the MX swamp and look for a way to drag the missile out to the high ground.

He agrees with Weinberger that the Soviet threat is real and with Pentagon research director Richard D. DeLauer, an old friend, that the way to respond to it is with quality rather than quantity.

But only time will tell whether this colorful addition to the Reagan team will have any more success than his equally confident predecessors in convincing Congress and the public that the Pentagon is getting as much bang as possible out of the taxpayers' buck.