As Trump took the stage just after 17:00 EDT (22:00 GMT) at a mega-church in Phoenix, the temperature was 111F (44C).
It was his first rally since his criminal conviction in a New York hush-money case, which found him guilty of falsifying business records in relation to a payment to adult-film actress Stormy Daniels.
Trump used the campaign event to repeat accusations that the case against him was politically motivated and called for the conviction to be overturned.
"I just went through a rigged trial in New York," he insisted. "It was made-up, fabricated stuff."
The ex-president is expected to appeal against all 34 charges in the trial.
Fans started lining up early outside the massive Phoenix Dream City Church to see him speak, and strict security measures meant it took time for everyone to get in.
Trump is next expected to hold a campaign event in Las Vegas on Sunday.
That city is also seeing record temperatures. The forecast high of 112F (44C) in Las Vegas on Thursday would be the city's earliest observed 112F day on record.
Temperatures are 20 to 30 degrees Fahrenheit above average for this time of year, according to the NWS, though they will cool slightly by the time Trump visits on Sunday.
The intense heat has placed more than 30 million people across the south-west region under alerts for dangerously hot temperatures, with officials asking residents to take precautions.
Heat-related illness and even death are becoming more common in Phoenix and the American south-west.
While heat domes were once described as rare, heatwaves and heat domes are becoming more common and intense because of human-induced climate change, scientists say.
The world hit 12 straight months of record-high temperatures, the European Union's Copernicus Climate Change Service said earlier this week.
Last month was the hottest recorded May in history.
On Thursday - two weeks before summer even officially starts - the National Weather Service (NWS) forecast record-breaking temperatures in interior California, and parts of Nevada and Arizona.
Temperatures were expected to reach 121F (49C) in California's scorching Death Valley during the heatwave.
In Phoenix, an excessive heat warning is in place on Friday, with people being asked to limit time outdoors and stay hydrated.
Trump started a small campaign tour with the stop in Phoenix on Thursday, exactly a week after he was found guilty in New York.
The former president spoke for about 90 minutes before departing for a fundraiser in San Francisco.
As well as railing against his conviction, he said he would reverse President Joe Biden's new executive order aimed at curbing migrant arrivals at the US-Mexico border.
"On day one of my administration, I will be rescinding Crooked Joe's outrageous executive order," he said, describing it as "pro-invasion".
The presidential candidate promised to "terminate every single open-borders policy of the Biden administration".
As both sides continue their campaigning, Trump said in an interview aired on Thursday that he would announce his pick for running mate at next month's Republican National Convention, commenting: "We have some very good people."