CAMBRIDGE, Mass. — Father J. Bryan Hehir, the former head of Catholic Charities and of the Harvard Divinity School, arrived a smidge late Thursday to the Kennedy School class he teaches on the ethics of war, and tried to jump straight into his planned lecture on humanitarian military intervention. His students, however, had other ideas: “Can you talk about the pope, please?” one asked.

Hehir is one of the most interesting thinkers in the church, so of course he could: When the charismatic John Paul II first stepped out onto that loggia overlooking St. Peter’s Square right after he was chosen to lead the church, he thought, “he overwhelmed the crowd.” When scholarly Benedict ventured out onto the balcony, “he taught the crowd,” and when humble Francis “stepped onto that platform, he related to the crowd.” What that shift will really mean, for and far beyond the world’s 1.2 billion Catholics, no one knows.

But Hehir’s surely right that there’s another decision, still tba, that will tell us almost as much about what to expect as the papal pick itself did: Who will surround Francis at the Vatican? And specifically, who will serve as his secretary of state — in effect, as his prime minister?

Nothing in the former Jorge Bergoglio’s background suggests a CEO pope in the making, and the new pontiff has no track record on the clerical sex abuse issue. “He will not be able to fix things by himself,” Hehir told the class. No one could, of course. “And as you know from this school, good government is about choosing those around us.”

The secretary of state Francis chooses will tell us nothing less than how determined he really is to make the kind of sweeping administration, institutional and bureaucratic reforms it would take to stop years of infighting and prevent more scandals of the sort that weren’t just embarrassing to the Vatican, but ruined many lives, and finally undermined the institution of the church itself.

The last two Vatican secretaries of state, Cardinals Tarcisio Bertone and Angelo Sodano, played significant roles in the abuse scandals, and are perfect examples of whom not to pick, and what not to do.

Sodano made sure that, as Jason Berry has been writing for years in the National Catholic Reporter, the Vatican had one set of rules for abuse involving priests, and another for abusive bishops and cardinals, who have regularly been allowed to step down without even losing their titles.

“Bishops are not stripped of their titles because to do so would violate the embedded logic of apostolic succession, that bishops are spiritual descendants of Jesus’s apostles,” Berry wrote in NCR three years ago. “Fattened by hubris, the tradition of apostolic succession has forgotten about Judas, who betrayed Jesus.”

Even another papal contender in the recent conclave, Cardinal Christoph Schönborn, of Austria, publicly accused Sodano of blocking an investigation into his abusive predecessor, the late Hans Hermann Groer. In Schönborn’s account, then-Cardinal Joseph Ratzinger wanted to sanction Groer, but Sodano and John Paul overruled him.

It was also Sodano who so energetically protected Father Marcial Maciel, the late, prolifically abusive founder of the Legionnaires of Christ, long after he’d been credibly accused. There may have even been a quid pro quo involved, since as Berry — who all Catholics who want a cleaner church owe a a big grazie — has also reported in NCR, Sodano took at least $15,000 in cash gifts from the Legionnaires, as personally arranged by Maciel.

Even when Benedict finally moved to ban Maciel from public ministry in 2006, Sodano managed to soften the wording of the announcement, and allowed his followers to spin his “acceptance” of a life of penance as selfless and Christ-like. Within weeks of Maciel’s departure, Sodano himself was replaced — but by another cardinal who’d strongly supported Marcial Maciel.

Is there a big enough broom in all of Rome to remove the years of built-up, ground-in grime inside the Curia? You won’t see Francis on the cover of Time with one in hand, a la former DC public schools chancellor Michelle Rhee. And he won’t, as Hehir joked, be signing up for any Kennedy School executive ed course, either.

But if Francis brings in someone untainted by alliances with Sodano and Bertone, that will be an important sign he means business. And if Robert Finn, found guilty in court last year of protecting a priest arrested for possession of child pornography, is still the bishop of Kansas City in a few months, we’ll have started to suspect that he doesn’t.

Melinda Henneberger is a Post political writer and anchors She the People. Follow her on Twitter at @MelindaDC.