Sorry for the delay. The Bose system uses an amplifier to boost the sound output before the speakers. Your amplifier is likely bad. Obviously there is output from the radio since the rear headphones work, as you already noted.
First, check the Amplifier fuse in the rear fuse panel. This fuse panel is under the rear seat (2nd row) on drivers side. Should be fuse #11. If the fuse is okay then the amplifier is going to need to be replaced. The amplifier is located in the passenger rear, behind the plastic side panel.
The problem with your temperature readout being incorrect is likely due to a failed ambient temperature sensor. This sensor is located in the fan shroud, behind the front grille.
If you would like any additional information or have more questions please don’t hesitate to ask!
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