heck, here I was thinking you had a bare cell. This thing most likely has a built in protection circuit - If it has a CE sticker, it's gone through at least some testing, if it has a UL sticker then it's gone through a heck of a lot of testing.
There's two possibilities, either the third pin is simply a thermistor (probably connects to ground), or it is a single wire interface to an on-battery protection/counter chip - google for "HDQ" or "SDQ". Short of opening up the battery, it would be hard to figure out. "Intelligent" batteries usually have the temperature sensing built onto the controller chip, and only accessible through a software protocol.
In any case, If you discharge the battery down to ~2.5V, the battery will either keep on dropping (i.e. it's not protected), or it will suddenly go open circuit. When you charge it back up, it should accept the charge current properly and reconnect itself. Dropping the voltage to 2.5V does damage the battery a little bit, so it might just be easier to (carefully) open up the battery...