Firing Belichick mid-season would be one of the all-time most disrespectful things any front office has ever done to a coach. I don't even like him, and I despise the Patriots, but them firing him, at all for any reason, would piss me off.
No, that's a guy that you first politely ask what his plans for the future are in the offseason, gauge whether he was thinking about moving on himself, and if he's not, then go through the process of saying you're moving on without him, in the most respectful way possible.
Good for them. Go win that division. Go win some playoff games. Start putting a pile of cheese on your coneys.