Yeah, I forgot these have sensors too. So I guess it would have to be a DC power supply. One problem might be the high wattage compared to voltage. Most 3.7-ish DC power supplies have no more than 2A for maximum current. Which is not enough wattage to power this.
I guess since it runs on only 1 battery and takes about as much as 3.7 squared Watts to heat up enough, it is safe to say it's a subohm heater, or at least very close to that - I assume not more than 1.2 ohms (which would be 3.7*3.7/1.2 = 11.4 Watts). We've also seen it, it's a wire coil, jsut like in sub-ohm e-liquid tanks.
And those can be tricky to power.
And also you must have very good wiring and contacts, or they would heat up too.
And I've seen him complain about the batter holder overheating, so it makes sense.
And also he said that different of supply wires can affect the temperature - another sign that the heater is sub-ohm. High-resistance devices shouldn't be too dependent on input wires and contacts.
That's becasue with a low-resistance heater, the low resistance of the wires and contacts and internal supply/battery resistance stops being insignificant compared to it. And you have to make sure they are high-quality and can handle that.
So I guess I was wrong - making a power supply for this is not going to be easy at all, unless he can find a supply that can really work with sub-ohm loads. Making even jsut the battery holder work can be difficult.
For example if the heater has 10 ohms and the supply circuit has 0.1, then 99 percent of the heat the circuit makes will be made in the heater. If the heater was only 0.3 ohms, then 25 percent of the heat would be generated in the suppyl circuitry - the wires, contacts, batteries or inside the supply. The more resitant parts heating up more than the more conductive ones.