Please, don't cut Bose any slack. They deserve to be shamed.
If someone were to make a self-exploding car, they'd be out of carmaking very fast. If Bose can't make headphones that don't self-ignite, they should not be making headphones.
Consider that Bose is breaking the law if they don't report this incident to CPSC[1].
And if you have a spare minute (which you seem to, given that you wrote the post and comment), please file a consumer safety report[2] and report the Bose QC-35 II headphones as unsafe product.
It is a simple form, and it is the way to make sure that this doesn't happen again to someone else. Aside from that, consider filing a lawsuit to get compensated for the damage to your physical health. Talk to a lawyer that can take your case pro-bono.
Thank you for the time you took to report this here, and I am very sorry that Bose screwed you over like that. Please let me know if I can help with the CPSC report to prevent them doing this to others.
[1]https://www.cpsc.gov/Business--Manufacturing/Recall-Guidance...