Hello Fallingwater,
Li-Ion cells are rated for a mid point voltage of 3.6 or 3.7 volts under normal loads. In high draw applications, it is best to try to keep the voltage around 3.5 volts. When the mid point voltage drops below that, the cell heats up, a lot.
If you don't value cycle life, and have unprotected cells, you can run them under a load that gives a mid point voltage of 3.0 volts, but you should provide cooling for the cells under those loads. Cell temperatures, under those kinds of loads, will exceed 145 F in the open air. The temperature will be higher if you enclose the battery, and the exponential increase in temperature may get you into a thermal runaway situation.
Most Li-Ion cells will handle a load equal to twice the actual capacity of the cell, but don't expect high cycle life from them.
Tom