Mine run in balance mode constantly so the length of time is not the issue.
Disagree, I don't think you can rule out someone's experience with just your own. It was an issue for me and I have read others with similar experience where the mosfets overheat and the unit is 'too hot to handle' and/or shuts down (as it should). Common problem....? I don't know.
From what I can gather from the post there are potentially two issues:
1 - A bum cell which is being replaced by the vendor
2 - Unknown BMS issue. Unsure what the orig. poster will do but I would not use that BMS without a careful review and monitoring or just replace it.
They are very lucky to have caught the fire before it got out of hand. It is a good reminder that any component that is leveraged in a DIY system should be vetted and any issues understood. In this case just replacing the cell and calling it a day would not put me at ease.