The only other hot-air engine fan currently known is the Lake Breeze fan, manufactured from 1915 to 1921 by the Lake Breese Moto company of Chicago, Illinois. USA. (there are various dates given on the Net)
Just below the bottom of the fan guard small vertical fins can be seen around the stem; these were to help cool the cold end of the displacer cylinder. They don't have much surface area and cannot have been very effective.
Hot air engines don't start by themselves. A small knob on the back of the fan was given a twist to start it once the internals had heated up.
Two levers near the base release the fuel tank and wick burner which lies under the base. A copper plate behind the blades states:
"Important directions use best grade alcohol only, grain or denatured, NOT wood alcohol. oil with one drop only, too much oil will stop motor, keep cap over wick when not in use and renew wick each 5 days" A wick only lasts 5 days? That sounds less than convenient.
You can see a video of a Lake Breeze fan here. The fan starts running at about 1:15.
There is some more info here.
This fan seems especially subject to misinformation, probably because few people know how a hot-air engine works. One web page said the fan was driven by a gas turbine...