this is becoming an unhealthy interest ... but it's just too hot in the garden ....
looking at irons - most turn out to be curling irons or soldering irons
however for clothes
the average seems to be 500-1000 watts (that's 4 - 8amps) - some are higher.
1 duracell dd mn1300 is 14000mah which will deliver 800watts for approx 10 mins (absolute top estimate)
I can't see any battery operated device (even from lead acid cells) that would even have time to warm up enough to do transfers.
although the huge high powered torches 1-5000000 candles - do have reasonable sized battery power sources
In the old days
there were flat irons ... heated from a fire
these are easy enough to get from most antique fairs (although your baggage allowance will be halved!)
there were irons that used charcoal or coal embers.
getable .... but quite expensive
and there was a hot water version (which was used on silk)
there are cordless irons ... and it looks like at least one of those uses a big capacitor to maintain the heat ... but it only lasts seconds between charges
found this
http://www.lehmans.com/jump.jsp?itemType=PRODU CT&itemID=1093
back to the curling tongs
and I'm certain I've seen a solar powered thingy
a matte black metal panel which gets incredibly hot in direct sunlight .... but we are getting into sci-fi now
I honestly just can't see you gettind an effective one
I hope I'm wrong.
if you do find one .... please post the details
time for a magnum.