NEW YORK — Gillian Randell put one hand on the patient’s shoulder and tapped with her other hand, like a doctor palpating someone with bursitis.

Randell was listening for a particular crunching sound. Think Rice Krispies that need a little more milk.

She did not hear a snap, a crackle or a pop. Her diagnosis: "This is in good condition."

The patient was an almost life-size image of Theodore Roosevelt near the top of a floor-to-ceiling mural at the American Museum of Natural History in Manhattan. Randell, a painting conservation expert who was perched on metal scaffolding, said the problems were elsewhere on the 1930s canvas: It was plagued by dust and "delamination," which means the painted canvas had come loose from the wall.

Randell heads the conservation team working on a $2.5 million restoration of that mural and two others that are steps from the museum’s main entrance on Central Park West. Starting in the fall, the team will undo the work of earlier conservators, who pinned the murals back in place with flat wooden disks the size of salad plates. The disks were inconspicuous — they were painted to match the mural. But the goal is to remove them and reattach the murals to the wall correctly.

The mural project is one element of a major refurbishing of the section of the museum known as Theodore Roosevelt Memorial Hall, which is New York State’s official memorial to its 33rd governor and the nation’s 26th president. Among other things, the facade on Central Park West is being cleaned.

Roosevelt’s connection to the museum was something special. The museum’s original charter was approved in the parlor of his childhood home, on East 20th Street in Manhattan. His father was one of the museum’s founders, and young Teddy added to the fledgling museum’s collection by contributing a bat, a dozen mice, a turtle, the skull of a squirrel and four bird eggs.

But the restoration comes at a time when Roosevelt has been taking his lumps. James Bradley’s book "The Imperial Cruise: A Secret History of Empire and War" makes the case that Roosevelt’s policies at the beginning of the 20th century put U.S.-Japanese relations "on the dark side road leading to 1941." Evan Thomas’ "The War Lovers: Roosevelt, Lodge, Hearst, and the Rush to Empire, 1898" says Roosevelt was one of the loudest warmongers in the noisy buildup to the Spanish-American War and his own march up San Juan Hill.

The museum considers him the "conservation president." And the historian Douglas Brinkley, whose most recent contribution to the Roosevelt canon was "The Wilderness Warrior: Theodore Roosevelt and the Crusade for America," called him "one of the three greatest people I’ve ever studied in American history." (The other two were Teddy’s fifth cousin Franklin and Franklin’s wife, Eleanor.)

By cell phone from Alaska, where he was doing research for a book on Teddy Roosevelt’s moves to save huge stretches of wilderness, Brinkley described Roosevelt as "multifaceted," "complicated, "individualistic," "impetuous" and "impossible to pigeonhole." He also said, "I find it hard to live with a portrait of Roosevelt as a bloodthirsty imperialist," adding that the idea that Roosevelt cleared the way for Pearl Harbor was "revisionism run amok."

"What they" — Roosevelt’s critics — "don’t say is he was president for seven years, and America never went to war," Brinkley said.

"And it’s impossible to overexaggerate what Theodore Roosevelt did for the country" by setting aside more than 200 million acres for parks and other public uses, he added.

One reason Roosevelt took such an interest was the museum. "He would listen to their mammalogists and ornithologists," Brinkley said. "Roosevelt loved to have dinner with them, and they would explain the plight of puffins off the coast of Oregon. It would be like seeing a TV commercial about animals in peril. He’d go and declare a federal bird preserve."

"What he got from the American Museum were these detailed scholarly reports, almost like Ph.D. theses from wildlife biologists," Brinkley said.

And Roosevelt saw it as the American museum. "He was so nationalistic, he wanted that museum to be better than the British Museum," said Brinkley, who was an adviser to the renovation of the Roosevelt memorial.

The murals were a Depression-era Works Progress Administration project that gave the museum a new entrance with Roosevelt front and center. The muralist, chosen from among 25 entrants, was William Andrew Mackay, who also did murals for the Library of Congress, the Minnesota House of Representatives and the New York state pavilion at the 1939 World’s Fair.

At the museum, Mackay showed the Panama Canal on one side, Roosevelt’s African adventures on another and the Treaty of Portsmouth — Roosevelt’s claim to the Nobel Peace Prize — on a third. Roosevelt turns up in each, checking plans for excavation of the Panama Canal here, surrounded by animals in Africa there.

The museum, well aware that the murals were aging, had them studied in the 1970s, the 1980s and the 1990s and did some small remedial work. "The chief issue, the chronic issue, since the ’70s has been the delamination of the painted canvas from the plaster substrate," said Kim Lovejoy, a vice president of EverGreene Architectural Arts, the contractor hired by the museum for the project.

As she climbed the scaffolding, Lovejoy gave a short version of Art Restoration 101: The murals were painted in oil on linen canvas that was attached to the wall. With time, the murals separated from the wall in places. Dust accumulated where the canvas wrinkled.

"Fortunately," Lovejoy said, "the paint is generally quite stable."

So the pilot project is focusing on how to clean the murals and reattach them for long-term stability. After a plan is worked out, and approval is obtained from the city’s Department of Cultural Affairs, among other agencies, the actual restoration will begin in the fall. It will involve, among other things, what Lovejoy called "flattening techniques" to ease the canvas back into shape.

"It’s like high-tech ironing," she said. "It gradually softens the canvas so it goes into place. You can’t just crunch it down, or it might tear."