The supply voltage to the microcontroller and SD card is regulated to 3V. However, SD card write currents can peak at 100mA and you then normally see a drop in the battery voltage due to their internal resistance. When the batteries are depleted, the internal resistance is higher and the supply voltage will drop below 3.0V. We stop recordings when it goes below 2.8V.

The regulator is effectively just a voltage controlled resistor so excess voltage is turned into heat. If the supply voltage is too high it gets too hot. Any input voltage from 3.3V to 6.0V works okay. The upper voltage is limited by the temperature of the regulator, and lower voltage by the minimum 0.3V voltage drop across the regulator.

A single Li-Ion and three series NiMH batteries spend most of their time around 3.7V and work well. As do three series alkaline batteries which start at a higher voltage but show a more continuous voltage drop over their lifetime.