In 1967, Daniel Janzen proposed the influential, but largely untested hypothesis, that tropical mountain passes are physiologically higher than temperate mountains. I test his key prediction, the one upon which all the others rely: namely, that elevational range sizes of organisms get larger on mountains at increasing latitudes. My analyses use 170 montane gradients spanning 36.5 degrees S to 48.2 degrees N latitude compiled from over 80 years of research and 16,500 species of rodents, bats, birds, lizards, snakes, salamanders, and frogs. In support of Janzen's prediction, I find that elevational range size increases with increasing latitude for all vertebrate groups except rodents. I document additional lines of evidence for temperature variability as a plausible mechanism for trends in vertebrate range size, including strong effects of thermoregulation and daily temperature variability, and a weak effect of precipitation.