Meteorologists in Miami, it is fair to say, are accustomed to drama: sunny-day flooding, severe rainstorms, strong hurricanes.

So it is telling — and scary — that they seem at a loss for words to describe the extreme heat that the city experienced over the past few days, a full month ahead of summer.

“It’s completely crazy, what just happened,” Brian McNoldy, a senior research scientist at the University of Miami, said.

“It’s insane,” said John Morales, a meteorologist for ClimaData, a private weather forecasting and consulting firm, and a hurricane specialist at WTVJ-TV, the NBC station in Miami. “Not only is it insane, it is also dangerous.”

They were talking about the heat index, a measure of how hot it really feels outside, taking into account humidity along with temperature. The heat index reached 112 degrees on both Saturday and Sunday, breaking the previous daily record by an astonishing 11 degrees.

Sunday’s high of 96 degrees was also record-breaking, Mr. McNoldy said. Saturday’s high of 94 was one degree shy of that day’s record. All of this in May, normally a sufferable month in Miami compared with the three or four that follow.