The moderate global warming that has already occurred as a result of human emissions has quadrupled the frequency of certain heat extremes since the Industrial Revolution, scientists reported Monday, and they warned that a failure to bring greenhouse gases under control could eventually lead to a 62-fold increase in such heat blasts.

The planetary warming has had a more moderate effect on intense rainstorms, the scientists said, driving up their frequency by 22 percent since the 19th century. Yet such heavy rains could more than double later this century if emissions continue at a high level, they said.

“People can argue that we had these kinds of extremes well before human influence on the climate — we had them centuries ago,” said Erich M. Fischer, lead author of a study published Monday by the journal Nature Climate Change. “And that’s correct. But the odds have changed, and we get more of them.”

The study by Dr. Fischer and his colleague Reto Knutti, of the Swiss Federal Institute of Technology in Zurich, is not the first to attribute large-scale changes in extreme weather to human influence on the climate. But it is among the first to forecast, on a global scale, how those extremes might change with continued global warming.