Suddenly Alexander Palmer Haley is a folk hero.

An estimated 82 million viewers, third largest audience in television history according to ABC, watched the Tuesday installment of "Roots," the eight-part movie based on Haley's best-selling family chronicle and now he is besieged by well-wishers.

Earlier that day, outside City Hall - where Mayor Abraham Beame like dozens of other officials across the country declared "Roots Week" - a young police officer stopped Haley. His South Carolina origins still keen in his soft voice, officer James Montgomery pumped Haley's hand and said, "Hey, brother, that's a magnificent piece of work. You've made us all proud."

In Haley limousine nearby the driver, John Sticco, a lanky unemployed construction worker from Astoria Queens said he was thrilled to be driving the newly famous writer."I almost cried watching the show," he said. "I'm going to buy the book now. I think it's going to change the way a lot of people think."

Even a dental appointment didn't provide a brief recess from the frenzy, since the dental assistant praised "Roots" to the sky as she worked on its author. "All I could think was 'that's fine, honey, thank you kindly, but just watch that drill,'" Haley chuckled afterwards.

Requests for everything imaginable, from job recommendations to autographs, have been pouring into ABC, the network that gambled $6 million on the story in rough gallery form, and to Doubleday, the publisher that waited 12 years for Haley to complete the book, and to the offices of Haley's agent, his lawyer and his two brothers who live in Washington.

Yet, at this point in the "Roots" fever, what has touched him the most, said Haley, have been the small moments. A few nights ago Haley was signing books in the basement of Harlem's historic Abyssinian Baptist Church. In line was a women in her upper 60s, her face lined with years of hard work, her suit worn and her veined hands clutching a shopping bag ith seven copies of "Roots."

As she approached Haley she took seven crumpled $10 bills (a discount price; the book retails for $12.50 out of her bosom. Haley looked carefully at the woman, glancing at her shoes, which were falling apart. She looked him straight in the eye and said, "Son, don't mind. I'm not buying just books, I'm buying our history."

Through all the notices of his success, big and small, Haley generally remains unruffled though upon occasion he has cried when his lectures received a standing ovation. And he told one of brothers last weekend, "It's amazing the way people are treating me. It's almost like I'm a star."

Haley, 55, appears an unlikely hero. His face is mooth and puffy, eternally babyfish; his full head of short black hair is generously flecked with gray; his stomach sneaks over the belts of his conservative blue and gray suits.

But his storytelling powers have created the excitement and, as he divorced writer jokes, have "made me more handsome to the ladies."

At heart he's still 'Fesser Haley's son, Palmer,' the name they still call him in his boyhood home of Henning, Tenn. Both his parents were teachers. He retains the determined pride that small community instilled in him as the son of a leading family. And he retains the stoicism acquired in the arduous haul up from cook to journalist, during a 20-year stint in the Coast Guard, to internationally known author of Malcolm X's autobiography.

Around him throughout Tuesday ABC executives were crowing. "Alex," one shouted, tugging at his arm. "We reached 28 million homes on Sunday evening. Haley looked at his feet for a minute, smiled slightly, and said, "Oh, my god."

On Sunday, "Roots" had a 61 per cent share of the national television audience, on Monday 62 per cent (31,330,000 homes), on Tuesday, a 68 per cent share (31,900,000 homes) and the overnight statistics from the three major markets on Wednesday night indicated a 61 per cent share in New York, 70 in Chicago, its highest ever, and 68 in Los Angeles.

"People keep saying 'you're so easy going,' or 'you're so calm.' I'm no different than before," said Haley, slightly amused. "My only problem now is learning how to say no, how to slow down."

Not a chance - and Haley knows it. On Monday night, while it was snowing like crazy, Haley was not in front of a television but speaking to 3,000 people at Lincoln Center.He arrived an hour early, walked on the stage, looked at the rows of burnished gold seats and said, "Wow." Then he turned to his publisher and his lawyer and apologized: "Hey, I'm acting like a country hick."

For the next two hours Haley never paused once, as he recalled the meticulous way he researched the book and all the luck involved. While he is writing, he takes showers compulsively; and when he talks the sweat pours off his face - emotion, not nervousness. But he never takes a drink of water.

When his talk was over, he had to duck out a stage door, something he hates to do because he likes contact with people. "It has started," he admitted, resignedly. "I have trouble getting in and out of place now."

For the rest of that evening. until 2 o'clock in the morning, Haley relaxed at two small parties, the first a Doubleday-sponsored gathering at the Plaza Hotel, the second a late night supper hosted by Ponchitta Pierce, a black writer. Glancing at his lecture schedule for the rest of the week - Dallas to Wichita to Lavonia, N.H. - Haley guessed he wouldn's see "Roots" again until he was home in Los Angeles this Sunday. But he has seen it a dozen times.

Especially when a group of blacks are around Haley, there's an atmostphere of basking in the glow of a brother who has made it. At the Pierce party the guests, who included Gordon Parks Sr., the photographer, filmmaker and writer; Franklin Thomas, head of the Bedford-Stuyvesant Restoration Corporation, a man who turned down a Carter administration post; Lionel Hampton, the bandleader; and Bishop Joseph Francis of Newark, N.J., all greeted him like a conquering hero.

A small brandy snifter in one hand, Haley was asnwering a question raised about the pristine look of the village, Juffure, on television. "I wanted the village to look like an Eden," said Haley. "I wanted it to be symbolic of our beginnings."

Even the few devastating reviews of the television series have not provoked anger in Haley. "I feel whatever a peron says, that's how they feel. It's a business, criticism. I'm not going to get involved in controversy. I'm not interested in winning skirmishes. I'm interested in winning the war."

The war he's waging, explained Haley, is for "Roots" to renew serious discussions about race relations. Haley, who has accepted the responsibility of a black spokesman role all the current attention has caused, feels, "all of this has opened a boil and let the pus come out."

Whatever the social outcome, the fame the work has brought, and the monetary success, appears to be agreeing with him. This week Haley looked more relaxed than he did four months ago when he was promoting the book, though the only rest he's had was a three-week journey on a freighter, which he spent writing mini-biography on President Carter for a post-Inauguration booklet.

The activity around Haley never slowed down this week. On Tuesday morning, with the telephone ringing constantly, Haley had a photo session, an interview with a correspondent for an African magazine and the dental appointment.

At noon he spoke before the Dutch Treat Club, a decade-old, all-male institution of media and entertainment personages. Although the group has a strict rule that no one can speak beyond 2 p.m., Haley spoke until 2:25. None of the 150 guests left.

Afterwards Isaac Asimov, the prolific science and science-fiction writer, was apologizing for not having read the book or watched the television episodes. "I'm afraid it would raise too much bile, too much anger in me. It's had an overwhelming effect on people and I will read it," he said.

Skitch Hendeson, the bandleader, clutched Haley's hand and told him that Ruth Steinway, the grande dame of the piano family, had given him his copy of "Roots." Henderson said, "I can't find the words to describe the effect it had on me."

In one corner A Doubleday executive observed the crush and said, "Well, at least they're not confusing Alex with Arthur Haley anymore. Now, in fact, we're starting to get Haley's mail."

By the end of this week the reactions to "Roots," its author and televison adaptation, are beginning to reflect broad and interesting impact on American society. Haley was made an honorary Texan by the members of the state legislature. Elsewhere, according to compilers at ABC, a Los Angeles disco "The Speak Easy" ahd closed for the week so its patrons can watch "Roots," a Sacramento restaurant reported business was off 40 per cent and a Bronx N.Y. medical center claimed their nighttime clientele had drastically dropped this week. And the hard-cover edition of "Roots," with 800,000 copies in print, is reported to be selling at a rate comparable to "The Final Days" and "Gone With The Wind," the 1939 movie adaptation of which is the only television event to top the estimated Tuesday ratins of "Roots."

Back at the hotel, a friend from the Carnegie Foundation, a photographer, a radio reporter, a resident of the Gambia and two cartons of books to be autographed, all waited.

When they left, Haley, his tie loosened, the ever-present cigarette between his fingers, glanced around at the three suitcases to be packed (one answer) and said, "This is all getting to be very crazy. I don't know when those people asked for an interview. I don't even know who they are." But Haley, the sensation of the motioon, hadn't thrown them out; he had talked to them for 30 minutes.

Everyone wondered what he had meant.

In rare quiet spells, when all the autograph seekers are gone, Alex Haley says he feels like "a total man." He hopes he's helping many others to feel like "total" human beings. "We have in this country obscured slavery. To some it's just a word. But no one has really dealt with it. Slavery set in motion two centuries of methodical stunting, a repression of a whole people to have equality. It's time for that to end and 'Roots' has moved us all. When I talk and when I cry the tears are for the whole thing - the gamble paid off. It has paid off way beyond the money."