The distinctive black and white hide - so the theory goes - provokes an intricate pattern of air currents and eddies that keeps the beast cool under the relentless African sun.
Because they retain heat better, the black stripes get warmer than the white areas, creating small vortexes when the hotter air above the dark fur meets the cool air adjacent.
The result is one of nature’s most ingenious air-conditioning units and a marvel of natural selection.
Or more accurately, according to new research by Swedish biologists, nothing more than an old wives’ tale.
A team at Lund University set out to discover it the theory translated to the real world by filling large metal barrels with water and then covering them with the skins of horse, cattle and zebra with various black, white and grey striped patterns.
The barrels were placed in the sunshine and the water temperatures measured.
Not surprisingly, the black barrel became the hottest and the white barrel the coolest.
However, the striped barrel and a grey barrel of equivalent overall whiteness reached similar levels.
Using thermography, the temperature distributions of the barrel surfaces were then compared to those of living zebras.
The sunlit zebra-striped barrels were found to accurately reproduce the surface temperature characteristics of sunlit zebras.
The study found no significant core temperature differences between the striped and grey barrels, even on many hot days, independent of the air temperature and wind speed.
Professor Susanne Åkesson, who led the research, said: "All these experimental findings provide evidence against the hypothesis of cooling effect of zebra stripes, because striped coats do not keep the core temperature of the body any cooler than homogeneous grey coats with a similar average whiteness.
"The stripes didn't lower the temperature.
“It turns out stripes don't actually cool zebras."
The apparent failure of the theory is the latest turn in an academic saga which has consumed biologists and natural historians for centuries.
Other prominent explanations claim the zebra fur thwarts attacks from biting flies, that the stripes help protect the animal from predators by visually confusing them, or that they are the result of natural “sex selection”.
The latter two theories formed the basis of a robust debate between Charles Darwin and rival naturalist Alfred Russel Wallace.
In The Descent of Man, Darwin rejects the idea the hide could act as camouflage, quoting the explorer William Buchill’s description of a herd in support of the sex selection argument: “Their sleek ribs glistened in the sun, and the brightness and regularity of their striped coats presented a picture of extraordinary beauty, in which probably they were not surpassed by any other quadruped", he said.
Wallace, however, supported the camouflage argument, pointing out that zebras were at most risk of attack at watering holes at night, when their black and white stripes could help blend the animal into the background.
Professor Åkesson explained how modern technology had leant weight to the air-conditioning theory.
"This hypothesis seems reasonable, because in sunshine the black zebra stripes are warmer due to their stronger absorption of sunlight compared to the cooler white stripes of higher reflectance,” she said.
"Infrared photography of zebras showed that sunlit black stripes are warmer than sunlit white stripes and that the difference between them increases with rising air temperature.
"At night, however, temperature differences are reversed, with black stripes being cooler than white ones."
The study is published in the journal Scientific Reports.