We had one of those sliding door dog door inserts for about 5 years. It was always cold around the door, and in the room with the door, and I can only guess how much money we wasted in heating because of it. It was really the only option in our last house though due to the layout. Every winter I'd be packing on blue tape around it and the sliding door, but you cant do much about the flap. No matter what, it's a gaping hole to the outside.

We finally got a through wall dog door with two flaps at the end of this winter at our new house. That's the way i'd recommend if its an option. I can already tell its going to be much better in terms of the cold getting in.