One of the most talked-about ­museum shows of the summer couldn’t sound sleepier: an exhibition of 92 Impressionist paintings from the Art Institute of Chicago that opens at the Kimbell Art Museum in Fort Worth, Texas, on June 29. So why the fuss? The Art Institute is charging the Kimbell an estimated $2 million for the exhibition. The remarkable fee has sparked debate among industry watchdogs, who say that museums should be allowed to recoup the cost of transporting and insuring loaned artworks but not, as the A.I.C. appears to be doing, make money.

“The A.I.C. is not an A.T.M.,” says Los Angeles Times art critic Christopher Knight, a three-time Pulitzer Prize finalist who writes frequently about museum ethics. “I have no objection to museums covering their costs through loan fees, but renting the collection for profit while pretending to loan it is just backdoor fundraising.”

Historically, charging outsize fees for lending exhibitions has been frowned upon. Art that’s in a museum isn’t supposed to be used to make money, the thinking goes. But in recent years, a few institutions have broken with tradition: While it was renovating, New York’s Museum of Modern Art charged for exhibits it sent to Tokyo, Berlin, and Houston. The Museum of Fine Arts in Boston and the Phillips Collection in Washington both raised cash when they sent paintings, most of them Impressionist works, to a gallery at the Bellagio hotel and casino in Las Vegas. The collection of Roman art from the Louvre, currently touring the U.S., has cost American museums as much as $1 million per venue. (View slideshow.)

Yet the A.I.C.’s $2 million fee is exceptional, and it seems even more curious in the context of the institution’s finances. At $700 million, the A.I.C.’s endowment is one of the biggest among American museums, and its $75 million annual budget has been comfortably balanced for years. A.I.C. director Jim Cuno says he entered the deal with the Kimbell to keep the works from sitting in storage while the A.I.C. renovates. The fee, he says, will cover the costs of printing a catalog and shipping the art. Some money will be left over, he acknowledges, but he won’t comment further, other than to argue that the arrangement isn’t a rental. “That makes it sound like it’s something that’s been motivated by some exchange of cash, as a means to gain some revenue,” he says.

With more than $1 billion in assets, the Kimbell can certainly afford to pay the A.I.C.’s asking price. What’s more, it’s a pretty safe bet the show will be a hit. The Kimbell’s last big Impressionist exhibition, in 1994, brought in 430,000 visitors, a record for Texas. Between sales of tickets, merchandise, items at the café, and thousands of new memberships, the show could generate revenue of $8 million to $10 million. Hence Malcolm Warner, the Kimbell’s acting director, takes the high road: “For us, the exciting new thing is just seeing one of the great Impressionist collections in the world in our galleries.”