That would probably interest a few people. There is a wireless glue gun sold in the shop just next to where I live, but it runs on butane. I wonder how much energy those heating elements would pull, and just how heavy the batteries would be to run something like that...
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This could be quite doable. I worked on some hand-held laser products where we would use a lithium-ion battery (2.1Ah @ 3.6V). We could pulse the lasers with approximately 100A peaks of current. We would PWM the laser (~50% at 20-30KHz) to create high energy bursts which would average out to about 50-60A for pulses of about 500-750mS with a pulse repetition rate of 2-3 pulses per second (allowing the battery and electronics to cool a bit). Worst case, this works out to about 30W, which is almost in the middle of the range for common glue guns (10 to 100W). A 2.1Ah @ 3.6V works out to about 7.5Wh, so at 30W watt rate you could get about 1/4 hour of on-time. Not great, but doable. Some cautions here, drawing this amount of current is possible, but you really have to watch the battery temperature. Our products would monitor battery temperature and limit pulsing to keep the battery in a safe range of operation.