Former Massachusetts Gov. Mitt Romney, right, and his former vice presidential running mate, U.S. Rep. Paul Ryan, R-Wis., on Thursday in Chicago. (Charles Rex Arbogast/AP)

Mitt Romney and Paul Ryan, sharing a stage and all smiles, reunited for a one-night-only show in Chicago on Thursday. The defeated 2012 GOP presidential ticket delighted a crowd of more than 300 die-hard supporters at the Union League Club with their chumminess and easy rapport, and stoked talk of their possible return to the campaign trail ahead of the 2016 presidential election.

In a joint interview, the pair sharply criticized former secretary of state Hillary Rodham Clinton, the leading Democratic contender for the 2016 nomination. Ryan proclaimed her “beatable,” and Romney panned her diplomatic record and suggested that she may not wear well with voters.

The evening, which was a promotional event for Ryan’s new book, “The Way Forward,” was not all serious, however. A few minutes before sitting down for the interview, Ryan, the 2012 Republican vice presidential nominee, doused Romney with a heaping pail of ice water to raise awareness for Lou Gehrig’s disease. “What’s going through my head? A bucket of cold water,” Romney joked.

“It was pretty good — and it’ll be on YouTube,” Ryan laughed.

By late Friday afternoon, the video of a dripping-wet Romney had more than 130,000 “likes” on Facebook and was widely shared on Twitter.

Former Republican presidential candidate Mitt Romney took the ALS Ice Bucket Challenge, with some help from his former running mate, Rep. Paul Ryan (R-Wis.). (Mitt Romney via Facebook)

Relaxing with Ryan before they headed off to different cities, Romney began by railing against Clinton, mocking her efforts to “reset” frayed relations with Russia early in the Obama administration.

“Looking at her record, seeing how ineffective she was . . . is going to be a great handicap for her in the general election,” Romney said. “I don’t think it’ll hurt her in the primary, but it will in the general.

“That picture of her with the foreign minister of Russia, smiling ear to ear with that red reset button, I presume that’s going to be an ad. Of all the miscalculations in foreign policy history, that stands out as an unfortunate one.”

His former running mate also played down Clinton’s odds. “She’s beatable,” said Ryan. “Her assets are her name identification, her ability to fundraise and her campaign experience. Her liabilities are policies and track record. She was one of the architects of the Obama foreign policy.

“I also think there may be a little fatigue,” he said. “People will be looking for someone new. She may be riding high now, but people may decide against having another four years of this kind of governing.”

Alluding to some of the unrest in the GOP over foreign policy — the friction between the camp of Sen. Rand Paul of Kentucky and those who seek a more muscular foreign policy — Romney said that now is “not the time for academic debates.”

“Our party has to come together, or we will continue with a third term of Barack Obama, with an agenda led by President Obama and Harry Reid,” said the former Massachusetts governor. “That agenda has led us to a foreign policy vacuum that is threatening the things we hold dear, including our own safety.”

With trail-ready rhetoric like that — along with a string of state-level appearances and robust candidate support — Romney has stirred GOP chatter about a possible third run for the Oval Office.

It’s a revival few could have expected. But Romney has seen his political capital rise in Republican circles over the past year, with the well-reviewed Netflix documentary “Mitt” and his many appearances for GOP candidates reviving his reputation in a party that never fully embraced him as its ­standard-bearer. Carefully picking where he campaigns, he has been able to play elder statesman and financial rainmaker in several Senate and gubernatorial races.

This month, Romney has campaigned in Arkansas, West Virginia and North Carolina. In September, he has visits planned to the presidential swing states of Colorado and Virginia.

Ryan has roused 2016 murmurs himself, particularly when he visited Iowa in April. But his pitch there seemed to be more about seeking to soothe the roiling divisions in the GOP than positioning himself for a presidential bid. He has not been to New Hampshire since January 2013. And his colleagues in the House GOP said his excitement about taking over the powerful House Ways and Means Committee next year is the clearest sign that his attention for the short term is on Capitol Hill rather than on making till-the-soil trips to early primary states.

Still, for a party that has no front-runner for the 2016 presidential nomination, Romney and Ryan are candidates who many see as natural possibilities, given their experience and lack of political baggage of the kind that has plagued such contenders as Gov. Chris Christie (R-N.J.), who has dealt with a bridge-closing scandal, and Gov. Rick Perry (R-Tex.), who was recently indicted for alleged abuse of power.

Speaking Thursday in Chicago, Romney and Ryan teased the audience by encouraging each other to seek the White House.

“Third time’s the charm,” Ryan said of Romney. Romney’s reply: Ryan “wouldn’t be a bad president” himself.

“As you see how things have gone, I think we’re at an ‘I told you so’ moment,” Ryan said later. “Mitt is being vindicated on foreign policy and on domestic policy. I think people are seeing that his projections were correct and the kind of person he is.”

He turned to Romney. “You know, I haven’t even told you this, but that documentary on Netflix gives people the view of the person we know,” he said. “It shows that we missed an opportunity to elect someone who would’ve been a great president. People seem to be reassessing.”

Romney continues to dismiss the likelihood of a third run.

“My posture, and I’ve explained this many times, is that I’m not running, but I hope Paul will give it thought, and there are other good people in the party giving thought, getting things organized,” he said. “I think you’ll see a very crowded debate in the first debate or two, and then hopefully narrow it down to someone who can express our vision to help the middle class in America and win in the general election.”