Instead of buying hand warmers, consider making your own. Thanks to peel-and-stick hem tape, they're no-sew. All you need is the tape, some fabric, rice, and scissors.
Rice has great heat retention, so these little guys will stay warm once you pop them into the microwave for 30 or so seconds.
uhmm...no, it doesn't work like that
fan has not enough pull power to suck the colder air from floor level, you need to force warm air that is stored on ceiling level down so it mixes with the colder
that is much more efficient way of heating up large air volumes