It would make EVs much more attractive for me, until charging infrastructure is more widely deploid, and allowing for a more gradual move away from oil.
Additionally it would at best be a benefit in hot climates where the battery needs cooling. In the cold you want to retain the heat not turn it inefficiently into energy.
Toyota's hybrids (Prius, etc.) have used Atkinson cycle ICE, instead of Otto (one maximizes fuel economy, the other power delivered, I heard).
Also, if your car can turn on its engine automatically, Stirlings and regular ICE have the same problem - Something is autonomously generating carbon monoxide and consuming your fuel without a human watching it. Spooky.