The 'T' pin is the thermistor safety pin, part of the 'Smart Battery Charger Interface' specification. It is used by the battery's control electronics to signal the device whether it is permitted to charge the battery or not. It allows the battery to cut off the charge if the battery is too cold or too hot.
It's kind of an unusual setup, but it was done this way to permit the construction of very cheap batteries. A battery need only connect a 103AT thermistor between the T pin and the ground pin and it will comply with the specifications, sensing only battery temperature. A smart battery can 'fake' a thermistor by permitting a controlled amount of current through.
If the resistance between the T pin and ground is between 2,850 and 31,500 ohms, normal charging is permitted. Restricted charging is permitted between 28,500 and 105,000 ohms (cold) and between 425 and 3,150 ohms (hot). If the resistance is under 575 ohms or over 95,000 ohms, the battery is too hot or too cold to safely charge. (The ranges overlap to provide some hysteresis.)