Agree with previous poster, something is definitely amiss here. I own a Ford hybrid (Fusion) as well, and know a little 'bout them.
With a Ford hybrid vehicle being flat towed, there is no way the gas engine (or electric motor for that matter) should EVER be able to come on, let alone come on and run enough to get the gas engine that hot! My guess is one of the following:
1. Something is seriously, seriously wrong with your C-max, and needs to go to the dealer ASAP to find out what.
2. Some how, some way, a blunder was made when hitching up, and the engine/drivetrain was accidentally left ON when towing.
If #2 is what happened, this could kind of make sense, why mileage was logged for the last 12 miles and overheated. With Ford Hybrids, generally the gas engine only turns on when either:
A) demand for power exceeds power electric motor and battery can provide, or
B) the batteries deplete low enough that gas engine engages to re-charge batteries.
If you accidentally left the engine/drivetrain ON when you hitched up, its possible the gas engine would not come on until the last 12 miles - That might have been the point where the batteries were depleted enough that it forced the engine to come on.
As to how/why the engine over-heated when it turned on for last 12 miles: Not sure on that, but given that Ford does NOT intend for that engine ever to come on when flat towing, nor do they intend for regenerative braking or most other electronic systems to be on when towing (and they may have been)....I can see how overheating might could occur under the conditions described.
Either way, whether you think you may have accidentally left drivetrain on when towing or not, I think I'd still take it to a dealer to be checked out.