I've had this nice Black Diamond LED headlamp for a while. What I didn't like about it was that a new battery cost almost as much as a new headlamp. Also, I couldn't use rechargeable batteries.
So today I modified it so that I could have a little pack of batteries in my pocket, with wires up to the headlamp.
The little battery that fits it is a 6V battery. So I set up a pack with four AA's, hook it up, and the thing immediately gets very hot. Even with three AA's it gets too hot. I now run it with only two AA batteries.
So why does that happen? Six volts is six volts even if the batteries have a potential of supplying more current. The current should be determined by the voltage, unless the small battery has a de facto limit on how much current it can supply.