Personally, I prefer using a box fan the break up stratified temperature layers in a room.
Forced air furnaces usually provide a powerful fan that mix up the air and make all the temperatures relatively equal despite their location in a room.
Forced air furnace design often takes return air for the furnace from the floor level, where it might be coolest, and also have warm air registers at floor level too!
Warm air registers are also commonly located under windows, which are often the coolest part of a room. Located there, warm air is added to cool locations.
But as I said, I like box fans. They are cheap, easy to clean, can circulate lots of air and are good at breaking up those stratified temperatures.
As Daksy says, most gas fireplaces, if they have a fan, take air in at the floor level and have it exit near the top of the stove.
Perhaps a reason for that pattern is that there is room and power for a at the bottom, where the gas valve and burner are commonly located, and the air can then be blown around the firebox above which is often a box within the larger box of the fireplace cabinet.
Also, at the bottom the fan and electrical connections are bathed in cool air being drawn in to circulate around the firebox. If the power and fan were at the top, they'd be exposed to the high temperature air produced by the woodstove, especially when the fan was turned off.
If you kept the fan in the bottom of the fireplace but directed warm air out the bottom, you'be be bathing the gas burner and electrical controls and wiring in a stream of warm forced air, which might not be a good idea.
But the ways of fireplace designers can be mysterious.....
