The projections, based on new computer models and reviewing what the scientists said was an "exceptional number of extreme heatwaves" in the past decade, are more alarming than the conclusions of the U.N. panel of climate scientists last year.
That report by the Intergovernmental Panel on Climate Change - the U.N. body that collates scientific research from around the world - merely said of heatwaves: "It is very likely that the length, frequency, and/or intensity of warm spells or heatwaves will increase over most land areas" this century.
Monthly heat extremes in summer - such as the heatwaves in Australia this year, parts of the United States in 2012 or Russia in 2010 - now affect five percent of the world's land area, the report said.
"This is projected to double by 2020 and quadruple by 2040," the scientists wrote of their new study in the journal Environmental Research Letters.
The tropics would be most affected by increased heatwaves, followed by areas including the Mediterranean, Middle East, parts of western Europe, central Asia and the United States.
"In many regions, the coldest summer months by the end of the century will be hotter than the hottest experienced today," unless emissions of greenhouse gases are curbed, said Dim Coumou, of the Potsdam Institute for Climate Impact Research.
The IPCC says heat-trapping gases, mostly from burning fossil fuels, are nudging up temperatures, and are likely to cause more severe downpours, heatwaves, floods and rising sea levels.
Almost 200 governments have agreed to limit global warming to less than 2 degrees Celsius (3.6 Fahrenheit) above pre-industrial times and plan to agree, by the end of 2015, a deal to curb greenhouse gas emissions.
Global average surface temperatures have risen by 0.8C (1.4F) since the Industrial Revolution.