I don't think the exact threshold is public, but it often seems to kick in when there are more comments than upvotes. The term to search for is "flamewar detector". Dan has quite a few comments that offer a little more information: https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu...

In general, the usual request is that questions like this one are better handled as an email to [email protected] than as a new thread. Dan is surprisingly responsive and usually willing to provide details if you ask.