A Stirling engine is quite large for the amount of power it produces. Not really suitable as a transportation engine, so I see why you only say you'll generate electrical power with it. They're also complex and difficult to start.

But it is true that it could operate on waste heat from the engine and so increase efficiency.

But you'd still have to charge your battery on those zero-degree F days and I don't think the Stirling would do it then, so you'll still need a complete charging system otherwise. So is it worth it to haul around a Stirling.

Actually, a Sterling engine will work better on cold days than hot days. The engine relies on the difference in temperature between the hot air and cold (ambient) air to work. The colder the outside air is relative to the exhaust, the more efficiently it will work.

I think the biggest disadvantage of this idea is that the Sterling is going to add a lot of weight and compexity to the car. I'm also not sure if it would really generate enough power to be worthwhile.