texas battery charger ic
Yes, slowing the rate of charge decreases the PNP temperature and the battery pack temperature.
When fast charging, they usually place a termistor or other temperature sensor inside the battery pack. This allows the charger to stop fast charging if the batteries get too hot. The MAX713 part will also stop fast charge if the batteries are too cold.
The AC adapter that you linked from Ebay will most likely do BOTH 12V and 5V. It appears to have a standard molex four pin disk drive plug. That standard requires both voltages although some drives only use the 5V section. I have a similar adapter for my USB to IDE drive interface. However, mine is only rated at 1.5A.
First test for the PNP getting too hot is a simple touch test. Run the charger for a minute or two on a discharged battery. Turn it off and quickly touch the heatsink. If it burns your finger, its too hot. Assuming its not buring hot, run it while longer and attempt to hold the heatsink. The heatsink should get hot and may even be too hot to hold. How hot is too hot is tough to determine. The junction of the transistor is rated at probably 125 degrees C. However, the case is far removed from the junction. Check the transistor manufacturer's datasheet for recommended case temperatures.
The minimum wall-cube voltage depends on the type of wall-cube you use. The ones with a 60HZ stepdown transformer will see the output voltage drop as the low increases. The one with a switching power supply will have a very constant regulated output voltage which is mostly independent of the load current. I would probably start with 12V as the minimum which makes R1 closer to 1.5K. If during testing you find that the minimum is lower, you can always recalculate and replace R1 with a better value.
You may want to check the datasheet for your batteries for the highest battery voltage during charging. According to the MAX datasheet, this voltage can be as high as 1.9V per cell for some batteries. The wall-cube voltage must be greater than (max battery voltage * number of cells) + 1.5V. For the 1.9V case and six cells, you would need 12.9V minimum. I suspect that fast charging would be aborted if this minimum is not mantained.
(I know the rated voltage of the cell is 1.2V, however this voltage is higher during charging to basically force current back into the battery.)