His presidency is winding down. A contentious election—fought largely over his rec­ord and legacy—is about to be decided. With that in mind, Barack Obama recently invited the presidential historian Doris Kearns Goodwin to the White House for a long, personal, open-ended conversation. The meeting, arranged by Vanity Fair, took place in the president’s private dining room, just off the Oval Office.

Doris Kearns Goodwin is no stranger to these precincts. She has been in and out of the West Wing ever since 1967, when, as a 24-year-old White House Fellow, she worked closely with Lyndon Johnson during the last year of his presidency (and then afterward as he wrote his memoirs). She has earned a raft of literary prizes, including a Pulitzer, for books about J.F.K., L.B.J., Franklin Roosevelt, Theodore Roosevelt, William Howard Taft, and, most notably, Abraham Lincoln—the subject of her landmark history, Team of Rivals, whose title gave America’s political language a new and permanent catchphrase. (Steven Spielberg would use Goodwin’s book as the basis for his film Lincoln, and when Daniel Day-Lewis won the 2012 best-actor Oscar for his portrayal of the president, he entered the Vanity Fair after-party with the author in tow.)

Goodwin likes to tell the story of the day in the spring of 2007, when a young Illinois senator phoned her, out of the blue, requesting that they meet because he’d just finished reading Team of Rivals. That call would begin a friendship. Since taking office, Obama has occasionally invited Goodwin, along with a small cohort of presidential historians, to come to the White House to discuss past presidents, their legacies—and his. And over the years she has had the president’s ear and provided historical context and, on occasion, counsel.

In their conversation, the president and Goodwin exhibit an easy camaraderie, sometimes completing each other’s sentences. They touch on everything from comedy Web sites to bodysurfing in Hawaii. But the central focus is on history, and on enduring questions. What is presidential temperament? How does a leader maintain perspective? When does the job of president feel the heaviest? What is good and bad about ambition?

Obama and Goodwin spent more than an hour over coffee, water, and scones (“I won’t be eating those,” said the president), followed by a brief chat in the Oval Office. Obama, in shirtsleeves, sat in a straight-backed chair, his long frame relaxed, legs crossed, as he responded or parried—always thoughtfully, sometimes intensely. ...