If you get a Peltier cooler, and heat one side while applying
a flow of air to a heatsink on the other side, it will put out low
DC voltage at high-ish current. Into the right kind of load.
So, that'll work from any battery that can heat a resistor and
maybe run a coolling fan.

Well, you DID say 'any thoughts'.

Seriously, do you have any accuracy requirements? AC or DC?
Any preference on battery type (palletload of lead/acid, or
single hearing aid cell)? Duty cycle? Battery life under load?