WINDHAM, N.H. — Undaunted by controversies that have dogged him in recent days, Donald Trump landed in this battleground state Saturday night for a rally attended by hundreds of exultant supporters packed into a sweltering high school gymnasium.

“The last time I was here, we won,’’ Trump said, standing at a podium before a backdrop of American and New Hampshire flags. “And we’re gonna win again.’’

The Republican presidential nominee arrived at Windham High School shortly after 8 p.m., and delivered a wide-ranging speech that touched on such subjects as the Iran nuclear deal, the Islamic State, and China, but he repeatedly returned to attacks on Democratic presidential nominee Hillary Clinton.

Trump zeroed in on Clinton’s recent admission that she “short circuited’’ when describing the truthfulness of her remarks to the American people about her private e-mail server.

“Unstable Hillary Clinton — you saw where she basically short circuited? She short circuited. She used the term,’’ Trump said. “I think that the people of this country don’t want somebody that’s going to short circuit up there.’’

He said Clinton lacks the temperament to serve as president, in apparent reference to similar criticisms she has lobbed at him.

“I have a winning temperament,’’ he said.

Trump also frequently highlighted his promise to secure the country’s borders from immigrants entering the country illegally, particularly from Mexico.

“Build that wall!’’ the crowd chanted in response.

Trump highlighted his endorsement from the National Border Patrol Council, which represents 16,500 agents patrolling the country’s southwest border. In its March endorsement, the union described the dangers Americans face from drug cartels.

“You know in New Hampshire maybe better than anyone … exactly what they’re talking about,’’ Trump said.

Supporters, many who had waited hours for Trump’s appearance, began to trickle out halfway through his speech, overwhelmed by the heat. Trump made light of it: “Everybody tonight will lose on average 6.2 pounds. It’s so hot in here,’’ he said.

Trump’s appearance came a day after he endorsed New Hampshire Senator Kelly Ayotte in her reelection campaign, despite blasting her several days earlier. Ayotte, a Republican seeking her second term, has criticized Trump for his comments about veterans and has said she will support but not endorse him.

Trump did not explicitly reference Ayotte during his speech but called for party unity.

“Even if people don’t like me, you gotta vote Republican, because we’re gonna pick great justices,’’ he said, in reference to the empty seat on the Supreme Court. “Our Second Amendment is totally under siege.’’

Trump concluded his roughly hourlong speech by describing how he would make America so great that New Hampshire would have to send a delegation to Washington to ask him to “stop winning.’’ The crowd jumped to its feet, roaring with approval.

Trump last visited New Hampshire in June. He won the first-in-the-nation primary there easily in February, with 35 percent of the vote — 20 points more than his nearest competitor.

The rally caps off a trying week for Trump, in which he has fallen in the polls and has drawn the ire of several prominent Republicans, including Ayotte, House Speaker Paul Ryan, and Arizona Senator John McCain, for criticizing the parents of a fallen Muslim American soldier.

At a rally in Portland, Maine, on Thursday, Trump also painted the state’s Somali population as dangerous, drawing a rebuke from Republican Senator Susan Collins.

But many of the Trump supporters who lined up hours early to see their candidate said they are not concerned about the recent controversies.

“Not being a politician, he has a lot of rough edges. He needs to be groomed,’’ said Lynn Kimball, 59, of Dracut, Mass. “I think he’s been doing a lot better as time goes on. I’m not worried at all.’’

New Hampshire residents in line said they’re glad Trump endorsed Ayotte, as well as Ryan and McCain, for the sake of party unity. But they were clear that their loyalties lie with the presidential candidate.

“That’s fine with me. I don’t think it really matters,’’ said Jaden Arsenault, 25, of Hudson, N.H. when asked about Trump’s newly announced support of Ayotte.

Peter Price, 50, of Atkinson, N.H., said he thinks Trump’s delayed endorsement was a “wake-up call’’ for establishment Republicans.

“It’s good to have a little bit of constructive conflict’’ in the party, he said. “[Trump’s] efforts to hold back are a wakeup call to them. They’ve done nothing to reverse this crazy train wreck.’’

Former Massachusetts senator Scott Brown helped to warm up the crowd with a joke about the temperature. “I told them to turn up the heat a little bit to get rid of the losers,’’ he said.

He urged the crowd to vote Republican up and down the ticket in order to retain control of the House of Representatives and Senate, and to take the governorship of New Hampshire. He led them in another “USA’’ chant. And he riffed on the usual flashpoints — the Iran deal, President Obama, and Benghazi — to the crowd’s delight.

Trump’s visit to the Granite State followed two private fund-raisers at homes on Nantucket and in Osterville on Cape Cod.

Vivian Wang can be reached at vivian.wang@globe.com. Follow her on Twitter @vwang3.