Fonera in 3.3v
It is possible to power up the fonera directly in 3.3v, by bypassing the voltage regulator. This voltage regulator looses a lot of energy by dissipating more then 850mW in the form of heat:
Heat in electronics mostly comes from dropping voltage by converting current into it, in our case, the voltage regulator in the Fonera drops 5V to 3.3V at 500mA, resulting in the dissipation of 850mW. That’s right, we are dumping 850mW right into the atmosphere in the form of heat.
3 batteries in 1.2v (3.6v) should be enough to power directly the fonera. Nevertheless, a voltage regulator will be needed to provide stable voltage to the Fonera.