They migrate to Washington offices by the thousands with the first summer heat wave to labor in the fields of government, many at low pay or no pay and many living on Big Macs.Some go into debt for the chance.

They are the interns, traditionally college students who come here to see how the real world works outside the classroom while they stuff envelopes for their congressmen, type and file for a federal agency or keep tabs on legislation for a public interest group.

In the tight job market in recent years, the game has turned more serious, and interest in such work-learning programs has mushroomed, not only in Washington, the historical interns' mecca, but throughout the country, according to experts in the field.

"Students are taking their futures seriously, thinking about what's going to happen to them after they graduate. There is much greater awareness of the transition from school to the world of work," said Richard Ungerer, director of the nonprofit National Center for Public Service Internship. The organization publishes a directory of Washington internships.

Resumes that list job experience can give graduates a "foot in the door" to their chosen professions, and an internship - even without pay - can provide that edge over the competition, Ungerer said.

"It's that old Catch-22: you can't get experience until you get a job, and they won't give you a job unless you've had experience . . . Increasingly, employers are recognizing that unpaid experience when they hire," he said.

Michael Daisley, 21, of Greenville, S.C., is one of almost 3,000 interns working this summer on Capitol Hill. "I like politics a whole bunch. But I know you can't just come out with your B.A. and say, 'Hey, I'm into politics," he said.

Daisley worked in the Carter campaign and is working this summer in the office of Rep. james R. Mann (D-S.C.). He will be a senior this fall at Davidson College in North Carolina.

While summer intern programs increased dramatically about five years ago and have grown steadily ever curred in university-based programs during the academic year for credit toward a degree, Ungerer said.

A nonprofit organization called the Washington Center for Learning Alternatives, established two years ago is aimed particularly at serving such "Washington semester student from around the country.

WCLA has leased a 10-story apartment building at 1430 Rhode Island Ave. NW that can house about 300 students interns at relatively low cost - currently about $100 a month, with two students in each efficiency unit.

Finding housing they can afford is a major problem for interns in high-cost Washington. So is eating, they add with a game smile, "We go to MacDonald's a lot," said Susan Young, 22, a graduate of Illinois State who is living in the WCLA building while working as an intern for the U.S. Chamber of Commerce.

Young is living on savings and "some backing" from her parents. "But the kids who take out loans are pretty much hurting by the end of the summer," she said.

There are 171 colleges or universities nationwide signed up to use WCLA's services that include placement, supervision and seminars as well as housing, according to its founder and president, William M. Burke.

"We had 53 students come here in 1975, 153 last year and will have 225 next fall," Burke said. Any extra space in the apartment building is made available to students in other internship programs or students enrolled in local universities.

A variety of programs travel under the name of internships these days, and "there are 100 ways to find them," according to George Washington University career services counselor Paula Hoffman.

Interns themselves come in all ages and inclunations. Some are chosen through competition and other because they have the right connections. Some work as "go-fers" while others are given important tasks.

The University of Maryland has a $12,000 program funded by the National Aeronautics and Space Administration for females and ethnic minorities. Selected high school and college students have worked in the program this summer with noted scientists on laboratory projects seeking a cure for cancer or investigating the origins of life.

Newspaper intern programs provoke keen competition. The Washington Post hires 20 college students each summer from about 1,500 applicants and pays them entry-level salaries. Most have had previous experience on other publications. "It's no vacation," said Post Assistant managing editor Elsie Carper. "They work harder and stay busier than they've been. They write a full range of stories."

Interns also are at work in courts, in laws offices, in the offices of lobbysits and in a range of other fields. In Washington, much of the work relates in some way to the federal government.

Although the interns find plenty to make fun of as they watch the bureaucratic machinery grind, some inevitably catch Potomac Fever and return to make their careers here. Some even return as member of Congress, noted Bill Byrd, staff director of Capitol Hill's Bipartisan Intern Committee.

Byrd, who has been working with Capitol Hill intern programs since 1963, guessed that at least 13,000 interns are working in Washington this summer.

The Bipartisan Committee provides the almost 3,000 Hill interns with orientation and a lineup of speakers - top government officials, members of Congress, lobbyists and journalists. Each congressional office hires its interns independently, and arrangements vary widely, Byrd said.

While many interns see this period as a chance to test the waters in their chosen field before they actually have to make a commitment, others plan to use their new knowledge in other areas.

Charlotte Pridgen, 27, is a Boston University graduate student in psychiatric mental health nursing who is working for a House subcommittee task force investigating health issues. She is one of 10 persons chosen from 100 competitors in a National League of Nursing program "to get nurses interested in health policy, more politically aware."

Pridgen said she is making contacts in Congress and plans to encourage her colleagues in Boston to give these contacts more feedback to use in making decisions on health issues.

Among the most eye-opening impressions of the Hill reported by Pridgen and other interns are the pressure and tension that precede a hearing, the "incredible piles" of constituent mail and the time expended answering it, the unexpected importance of congressional staff, the "fish-bowl life" of members of Congress and the various ways in which federal agencies interact with each other and with Congress.

"Someday, though, we may withdraw our cheap labor, and the whole government could collapse," cracked intern Michael Daisley.