The Corcoran's first air-conditioned exhibition in 113 years opens today. It should cool off not only its visitors, but some hot tempers among Washington artists.

After years of complaining that they've been under-represented at the Corcoran--and given no voice in deciding who will be exhibited there--the city's artists have been placed at the helm of an ingenious show titled "Ten Plus Ten Plus Ten: Washington Painting 1982." It was organized on the peer principle: 10 painters were asked to invite 10 others who, in turn, chose 10 more.

The Corcoran's curators, accustomed to playing the role of Christians before lions, can now sit back and watch the lions eat each other. If the 30 artists don't like this show, they have no one to blame but themselves.

But it's more likely there will be light shed than blood shed in this revealing and provocative show--even though some of the artists aren't quite up to the challenge posed by their peers.

The first 10 artists in the chain were chosen, says Corcoran associate director Jane Livingston, to represent different generations, styles and philosophies of artists who have not shown at the Corcoran. The original 10 are Yvonne Carter, Benita Berman, Robyn Johnson-Ross, Polly Kraft, Val Lewton, Keith Morrison, Jody Mussoff, Bill Newman, Stephen Pace and Robin Rose.

The show, sensibly installed on the buddy-system, by threes, lets the viewer examine the network of the artists' choices. Some show stylistic affinities, but most do not. Some have chosen colleagues, mentors or friends, while at least one, Benita Berman, has chosen the work of an artist she did not know personally--Jane Dow--because she "admires her adventurousness." Some chose painters more famous than themselves, such as Polly Kraft, who selected fellow watercolorist Patricia Forrester, who in turn chose Alan Feltus and his recent, mysterious, Balthus-like classic nudes. Feltus, who last exhibited at the Corcoran in 1973, is perhaps the museum's most glaring oversight in recent years.

The show that results from this unusual selection procedure consists of 90 works by 30 distinctly different painters--most of them little-known or just emerging in commercial galleries and alternative spaces here. Only one, Sam Gilliam, can be called famous, though several have established reputations. They run the current stylistic gamut from trendy Neo-Expressionism through new image painting, Realism, Surrealism and Abstraction of various stripes (except stripes) to high individualism. Together they suggest that Washington painting today is lively, varied and brimming with new talent, if not new ideas.

The show begins boldly with the paintings of Robyn Johnson-Ross, one of the strongest new talents on view, whose powerful, jagged figures throb with neo-expressionist passion. Her choice, Matthew Smith--still a very raw talent--paints in the same spirit, though in a wholly abstract vernacular. His giant, monumentally messy, unstretched canvases may cause more controversy than any others, though his choice of newcomer Aimee Jackson, a highly expressive new-imagist, is likely to go unchallenged as one of the real discoveries of this show.

Berman, another find, swiftly lightens the mood with her whimsical "Wall of Shirts," a piece-in-progress that consists of several small paintings of T-shirts. Berman's chosen artist, Jane Dow, will be as surprising to viewers as it was to Dow. Dow's are dark, mysterious paintings with nude silhouettes scratched into the waxy black surface--a follow on her recent show at Osuna. Dow's chosen artist, Gay Glading, is represented by three swirling drawings on fabric that burst with energy.

The American University faculty has stuck together in one gallery, where Stephen Pace's joyfully colored landscapes soar and colleague Robert D'Arista's small, dark paintings disappoint. A superb painter, D'Arista selected his own work, which all artists were allowed to do, but to his own disadvantage. If this show has a major flaw, it was the failure to insist upon curatorial consultation in making selections. Showing to high advantage is Jody Mussoff, whose drawings of people engaged in strange, semi-hysterical activities have now been replaced by paintings. The new medium adds substance to her work. "Girl with Cat," however, comes dangerously close to aping Francis Bacon, as does the work of Bill Newman.

In recent years, the Corcoran has been damned if it did and damned if it didn't so far as Washington artists were concerned. Under pressure from an angry and vocal segment of the art community, director Peter Marzio three years ago established a new position of Curator of Washington Art, which Clair List carried out, with increasing approachability, until last January when the angry artists cried "separatism" and the job was abolished. The artists complained yet again, and this show is the result, though the Corcoran's associate director Jane Livingston says it was undertaken "not in direct response to, but in a climate of turmoil in the Washington art community."

Whatever her motives--and those of List, who assisted Livingston in the organization of this show and its catalogue--the solution seems a brilliant one and the format might well serve an ongoing need in the future. The idea has occurred to Livingston, but director Marzio's view is see and wait. "We'll have to see how the artists and the public respond," he says, adding that local shows always have the lowest attendance at the Corcoran. The show continues through Aug. 15.