Love is how you act in spite of what the other person does, not because of it.
In the case of the lady leaving the jacket in the car, one should know that women tend to favor fashion over practicality. They wish to look nice; perhaps the jacket covered her fashionable clothing. How many times have I seen a lady in the grocery store, shivering over the frozen foods? She knows where she is going, she knows that it will be cold, but she wants to wear that fancy new blouse and doesn't want to cover it up with a coat. The thing to understand is why is the man acting like this? Perhaps what she did is foolish to you; it doesn't negate the fact that she is cold, and you love her. So, do you love her "because" of what she does, or "in spite" of it?
Give her the jacket.

David