18650 battery pack question?

Yes, temperature sensor most likely. Here's what I would do to diagnose:

1) Get a voltmeter, and put it across red and black. Should see high 3.x volts if the battery is charged.

2) Put the voltmeter across white and red, then white and black. Should show no voltage.

3) Switch the meter to ohms (maybe the 2000 scale or so), and see if you can measure a resistance across white and black, or red and black.

4) Warm the battery pack in the sun, then see if the resistance changes. If so, it's a temperature sensor.

If still unsure, you may have to cut away the plastic shrink molding to see where the wires go.

Most likely it is to do with safety considerations.

Get a schematic --- if you can find one --- for the speaker.

Otherwise, call the manufacturer of the speaker and ask.

Don't let them get away without telling you anything useful.

They DO have the info somewhere.

Powered speaker?

Depends which one. If stereo, Red is right audio + black (common); White is left audio + common (black).

Ground wire.