replacing old battery(3wires) by a 2 wires battery

After the odyssey of opening the ipod, the original battery with 3wires (red, black and white) was replaced by a 2 wires battery and it worked fine for hours.

Unfortunately it is no charging when plugged, and it seems a common issue for whose who has replaced battery.

Is ther any way to fake the temperature sensor through a shortcut?

maybe installing a resistor?

ideas?

The dimensions of required battery are not very standard or easy to find.