Wow, only 87°F? Feh, that would be way below average for summer here.
Those Dyson fans nearly drove me crazy trying to figure out how they worked from just images and the commercials. The local Best Buy had a working model on display and I was able to get an up-close look at it. There are tiny holes positioned all around the inside of the ring. The air current is generated by a screw-fan in the base of the appliance, forcing air up through the holes.
Also found this article about how the IPO rejected Dyson's first patent submission for the device, because the basic design was already patented in 1981 by a Japanese company who never manufactured the similar device.