The slow season. July, easing with great humid discomfort into August. The smart ones are at the beach or behind air-conditioned doors watching the Iran-contra hearings. But there's more to summer than reading a trash novel on the sand and watching Oliver North become the national-hero-of-the-moment. While most of the bigger art and cultural happenings are scheduled for the fall, there are lots of stirrings in the languid air all week:

Bed coverings might not be the first thing one thinks of in summer, but the DAR Museum has chosen to feature them in its new show of rare quilts -- some with bold floral patterns and exotic-bird motifs -- opening today. "First Flowerings: Early Virginia Quilts" will feature 20 quilts and counterpanes made in the state before 1840. The exhibit runs through mid-October.

Wienies as art? Barbecue as inspiration? An exhibit, now at the Glen Echo Gallery in Glen Echo Park, celebrates local artists' attempts to create art out of this outdoor tradition. Favorite work: Frank Herrera's "Barbie-Q," a gaggle of dolls in aprons, one Ken and a tiny grill.

Wednesday is the worst day of the work week: It's too late to get excited about the past weekend and too early to bolt for the next one. While a few pocket-sized parks provide an uplifting lunch spot on sunny days, it's likely to rain on Wednesday. So head inside the Washington Square building, at 1050 Connecticut Ave. NW, and check out the whimsical display, "Sculpture '87." The exhibit of contemporary sculpture from Maryland, Virginia and the District, with its bold and colorful shapes, will lift even the lowest spirits.

You can't get tickets to the Bolshoi Ballet's performances starting this week at the Kennedy Center. But you can learn all about the troupe in a lecture at the Smithsonian's Baird Auditorium on Thursday night by New York Times dance critic Anna Kisselgoff. She will discuss the history of the famous company and explain the background of its flamboyant and theatrical styling. (In other words, tell you about what you missed.) Tickets cost $6 for members of the Smithsonian's Resident Associate Program, $7.50 for nonmembers; call 357-3030.

On Friday, give in to the weather and check out the "Dog Days Dog Show" at the Kathleen Ewing Gallery, 1609 Connecticut Ave NW. The exhibit will feature paintings, drawings, photographs, ceramics, stained glass and jewelry -- all with the bow-wow theme. A percentage of sales will benefit the Washington Animal Rescue League.

The Women's Center of Northern Virginia will offer a Saturday morning forum, "Draw Me! Careers in Art and Design." Professionals from the fine arts, crafts and graphic arts fields will give the how-I-did-it talk to aspiring artists. The cost is $15; call 281-2657 for information.

Finally, on Sunday, relax and catch an outdoor concert. From 1:30 to 4 p.m. the Anacostia Concert Choir (gospel), Soda Bread (Irish music) and the Buck Hill Quartet (jazz) play at the Foundry Mall on the C&O Canal in Georgetown. Later, the Marine Band is at the Sylvan Theater at the Washington Monument at 8 p.m.

The Busy Building Museum

A flurry of news from the National Building Museum this week. The museum will begin a new education project this summer, continuing into the 1987-88 school year, called "Design Wise." The pilot program will attempt to create a national program for design education, integrating design concepts and skills from architecture, graphic design and product design into biology, social studies and the arts in local high schools. Included will be a four-day workshop with 60 high school students, who will analyze a changing neighborhood in Washington. The students will take photos of the site, interview residents, make plans and put on an exhibit. The results will be introduced into six schools in the fall.

Also, the museum's exhibition galleries will be closed until the end of September for construction work being done on the Great Hall of the Pension Building, where the museum is housed. The information desk will stay open to answer questions about programs and the Pension Building renovation, which is expected to be completed in 1988.

More on Money

Though there were long listings of new grants in last week's column, there's still more moolah being handed out locally:

The Washington Project for the Arts has received a total of $29,000 in three grants. The April Trust gave $15,000 for transitional support of the arts organization's programs as it grows; the Best Products Foundation donated $5,000 toward a fall exhibition, "War and Memory: In the Aftermath of Vietnam"; and the Gannett Foundation gave $9,000 to fund a catalogue for WPA's current "Options '87" exhibit and also a new brochure for the group.

The National Endowment for the Arts handed out more funds to local artists, including $6,700 to support the creation of "Invisible Harp," by Skip LaPlante. The work uses beams of light that make music as people pass through them, and will become an exhibit at the Capital Children's Museum. The NEA also gave $10,200 for creation and development of "Atomic Priests," an interdisciplinary work by choreographer Liz Lerman, poet Essex Hemphill, sculptor Ed Love and composer Richard Lerman.