Okay, just go through opening one up, and poked around some. An AC adapter won't charge your batteries, it switches when you insert the plug. Not much for components, 2 resistors to limit the current, and a bridge rectifier to make sure the fan only spins in one direction. Nice wiring job though, quality work inside the case.
Going to look for a higher voltage adapter, hopefully around 9-12 volts that will fit, or something to donate a plug. Pretty sure these can handle more power, and should get hotter or colder. Probably not boiling water or making ice, but not comfortable to the touch. Warm up coffee, or keep a beer ice cold...