It’s the height of summer, an ideal time for spending stimulating afternoons in air-conditioned museums. But if you yearn to be roused from your summer drowsiness at the Museum of Fine Arts, don’t assume they have your kind of coffee. The MFA is looking as sleepily provincial and as somnolent as I’ve seen it.

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The big summer exhibition is a show of prints highlighting out-of-date fashions and Maine landscapes by Alex Katz. Other current exhibits include “Grandstand to Gallery,” a collaboration between the MFA and Fenway Park; a small display of photographs of Queen Elizabeth II by perennial MFA favorite Yousuf Karsh; a show of Japanese prints called “Cats to Crickets: Pets in Japan’s Floating World”; and “Paper Zoo,” a potpourri of images of animals cheerfully retrieved from storage.

Surveying these offerings is like stepping into “Make Way for Ducklings.” To be so infantilized by any museum — let alone a museum of the MFA’s stature — is embarrassing. One of these kinds of shows would be fine. But so many?

I went looking for smaller shows I hadn’t yet seen, grown-up shows drawn from the museum’s astonishingly deep and rich permanent collection. I came up with two one-room exhibits in the Art of the Americas Wing.

Unfortunately, neither rises above the level of satisfactory. But if you’re already at the museum (and I’m certainly not trying to discourage anyone; this remains one of the world’s great museums), they might provide a few stimulating moments.

The first is “Art of the White Mountains.” That’s right: more lovely New England scenery. Chosen from the collection, it gathers together depictions of the popular and scenic mountain range in New Hampshire by artists from the 19th century to today.

The accent, mind you, is firmly on the 19th century. The artists include Thomas Doughty, Thomas Cole, Sanford Gifford, George Innes, and William Zorach. They, and a handful of other artists, are represented predominantly by paintings, but also by drawings and watercolors. There’s even a majestic black-and-white photograph by Bradford Washburn.

I liked best George Innes’s “Near Kearsage Village,” from 1875. The fir tree in the foreground is a marvel of representation: It’s not so much painted as shazam-ed into place. The color and tonal relationships between its alluring, dark green presence at center, the stark white trunk of the bare birch beside it, and the covering of light green grass on the tussocky hill in the foreground is transporting.

A recent MFA acquisition, Robert Duncanson’s “Lancaster, New Hampshire,” painted in 1862, is also impressive. It’s a small landscape, in portrait format, which Duncanson, the son of biracial parents, painted looking across the border from Vermont, on a trip from Montreal to his home in Cincinnati. The sense of space in this picture is vertiginous. It recedes deeply toward the mountains in the far distance, but it also flies up into a sky made palpable by a luminous tuft of cloud at top center.

David Johnson’s dry, cool colors make for a vivid and likable contrast, with the russet reds and effulgent golds in more artfully atmospheric paintings by Cropsey and Gifford.

And I was interested to learn that part of what drew the earliest artists to the White Mountains — in particular Thomas Cole and Henry Pratt — was a tragic true story: Threatened by a mudslide, the Willey family had moved to another building on their property for protection, but were subsequently killed by an avalanche. The original house, meanwhile, was left standing.

The White Mountains have inspired countless American artists over the years. But so have many other mountain ranges. The MFA show is all a bit too cozily local if you ask me. An otherwise unremarkable 1996 sketch by Andrew Haines, for instance, is included simply because it has a black fly squashed onto its surface — providing an excuse for the writers of the wall labels to insert a reference to this “notorious White Mountain nuisance.”

Not far away, on level three of the Art of the Americas Wing, one can see “The Allure of Japan,” a show about how Japan became a source of fascination in American art and design after 1854. That was the year in which Commodore Matthew Perry landed at Tokyo Bay and opened trade between the two countries.

The show kicks off with a remarkable hand-colored lithograph by William Heine, showing the Americans’ first landing. Heine was with Perry on this momentous expedition, and recorded the scene in sketches that were later turned into prints.

Of course, America wasn’t the only country to become engrossed in all things Japanese. The French were similarly affected. But there was a very active trade between America and Japan, especially after about 1870, and Boston, Salem, and other New England ports were hubs, overseeing the exchange of a huge array of goods, and seeing off many Americans undertaking business and pleasure voyages to Japan.

The show, like “Art of the White Mountains,” is drawn from the MFA’s collection, and it includes posters, prints, and even a cabinet adorned with an ensemble of ceramics inspired by Asian aesthetics.

“Asian” rather than “Japanese” because the cabinet itself is, in fact, in a Chinese style. At the time, the Japanese craze was not especially discerning about differences between these two great cultures, and tended to let them blur together. Should this show do the same?

It’s an open question. I suppose the problem with the exhibit, which has lots of fine things, is simply that the subject is so huge. As a result, the selections can seem arbitrary. There’s a wall of posters, for instance, but some of them have no connection with Japan beyond the fact that they are in the Art Nouveau style, and Art Nouveau was influenced by the Japan craze. It’s pretty tenuous.

Better are the pairs of prints — by both Japanese and American artists — that make affinities obvious but also show up differences. Mary Cassatt’s “The Coiffure,” for instance, hangs near Kitagawa Utamaro’s wonderful “Mother Nursing Child Before Mirror,” a woodblock print made almost a century earlier.

The connections — feminine intimacy, mirrors, flattened composition, asymmetry — hardly need spelling out. But of course, Cassatt, though American, was based in Paris, where “japonisme” was a subtly different phenomenon, and her work was mediated through the influence of Edgar Degas as well as her own experience as a Western woman.

Museum of Fine Arts

Kitagawa Utamaro’s “Mother Nursing Child Before Mirror” is in the MFA show “The Allure of Japan.”

It was instructive to see “Japanese Waterfall,” a watercolor by Lois Mailou Jones which repeats the waterfall motif as if she were making a design for wallpaper, next to Keisai Eisen’s woodblock print, made 80 years earlier, and showing a similar motif, but in a livelier, more original idiom.

And of course it is always good to see prints by Whistler, who was so profoundly influenced by Japanese aesthetics, next to some of the images that cast their spell on him. Here, Whistler’s lithotint, “The Tall Bridge,” hangs suggestively next to Utagawa Hiroshige’s woodblock print “Evening Moon at Ryogoku Bridge.”

Other works in the show suggest less potent influences: John Leon Moran’s “A Japanese Fantasy,” for instance, is just that: a Western girl wrapped up in a kimono. It’s a very slight thing, and a cliché — but that is the point of its inclusion. It’s not without its own delicate beauty, and it speaks to the manifold ways in which the thirst for exoticism can wind its way into art.

The MFA has been doing good things updating aspects of its permanent collection, even as other aspects stand in need of dramatic improvement. Its new hang of 20th-century American art, for instance, on level four of the Art of the Americas Wing, is a vast improvement on the inaugural hang.

With its new selections of work by Agnes Martin, Sol LeWitt, Sean Scully, Robert Motherwell, Louise Nevelson, and Robert Mangold, and, in a neighboring gallery, an inspired hang of Boston Expressionists alongside apocalyptic images by David Siqueiros, Jose Clemente Orozco, and Norman Lewis, all sharing space with the MFA’s two Jackson Pollock paintings, the museum is now presenting a cogent, intriguing (and death-haunted) argument about postwar American art — not just a baggy, yard sale aesthetic. It’s a wonderful transformation.

Unfortunately, by contrast, the temporary exhibitions this summer seem insipid.