There is no need to perform a core hack. Or at least you can perform a core hack by means of a plugin. Create an override plugin that overrides function qa_db_hotness_update in file qa-include/qa-db-hotness.php. I guess you could perform an update query that results in a boolean value to determine whether the question has more or less than X votes.
The downside is that I don't think this will only list the ones with more than X but rather this will list them first. Probably, that is enough for you and you don't need to filter the rest of the questions out. If it isn't you might need to modify how data is being selected in that page.
A different alternative, which is the one I would go for, is to disable the HOT section and create a new page plugin that filters only questions with more than X votes.