Do you think the following problem with my car is covered under a 5-year/powertrain warranty?

My car broke down on the parkway yesterday morning. I noticed that the heat stopped working 3 days ago, my temperature light went on yesterday, the car overheated and then stalled on the parkway. I drive a 2007 Ford Mustang with only 22K miles on it. This should not have happened at this mileage! Does this sound like a repair that's covered under my 5-year/powertrain warranty, and can I have my $230 towing charge reimbursed by Ford?