Either that...
...or the moderator can send the first flaming remark to oblivion while leaving the thread as it is.
This disrupts the thread, but it tends to snuff out a potential flame war at its initial point of combustion.
Threads don't move all by themselves because they reach a critical number of n/t posts or of naughty words, or for any other reason. For a whole thread to be moved because of flames, most of the people in it would have had to behave abominably. Removing offensive remarks one by one can be tedious, but it would be worth it.