advertised as 3.2v cells, not 3.6
3.2 volts in the nominal 'average' voltage over the working range.
As I stated in an earlier post, you have a short circuit on the power supply.
Check again that you have the cell polarity correct. Check your voltmeter against an AA dry cell to confirm its OK.
The wires are hot because of the short, that seems to be your cells. The power supply has hit the 10 amp limit.
I suspect the cells are incorrect connected, verify which is the positive and negative.
As I suggested, the parallel top balancing to often a way to damage the cells. There are many examples of disasters reported. I have outlined alternatives. Read post #5.
When things are not working out in any electrical system, take a step back, disconnect the everything. Then test each part independently. A 12v car bulb is a great test device.
Can the cells light the bulb? Can the power supply light the bulb? Test the polarity of the cells.
Many low cost off the shelf' batteries don't seem to have balanced cells as supplied, and after a period of use the BMS sorts out the issue.