Apparently the Australian minimum is 300mm from the ceiling, but that is probably about the safety issues... ie our minimum ceiling height is 2400, so with a minimum clearance of 2100 from the floor, that leaves 300mm to the ceiling. Are your ceilings insulated from the roof space? I think that would have the biggest influence on the temperature of air directly below the ceiling.
In any case it's worth noting that the main way that fans cool us is not by supplying cool air (unless the fan is connected to a cool air source, such as in an air conditioner) but by activating the sweat on our skins, so the best way to do that is to have a fan set to give a low air movement over your body which will just evaporate the sweat. Too high (which is the most common error when using them) and you initially feel cool then just feel the hot air flow once the sweat glands can't provide moisture fast enough; too low and you won't feel anything much.
[Although not part of your post's query:- For sleeping, I found that a floor-stand fan, set at low speed sweeping across the room was best, since it cools the body as the air passes over, then while its away the skin can replace the small amount of moisturise needed to cool down on the next pass over. I discovered this by I being raised in an old fibro house, no insulation of any sort, with long, hot summer nights. I slept ok. ]
