Is it common sense to sit in a freezing cold car while it is heating up, when you can make your breakfast instead.
I don’t believe sitting in your car will avoid the fine. You will still be “idling”
When I lived in Calgary, I made the mistake of starting my truck, one winter’s day, and immediately driving. Within minutes I had a coating of ice on the inside of every window from my breath. So I had to pull over until it heated up. After that, every winter morning, I started it up and went back inside for breakfast. Problem solved.