Cat door allows A/C to leak out

I rescued a stray cat off the streets of Birmingham, then i ended up moving the cat with me to a more rural location in Alabama! My cat is now my whole world. I was never a cat lover before, but I sure am now. My cat has her own room in the house. I have a queen sized bed with soft sheets for him to sleep on, then she has a immense cat tree, ledges, scratchers, posts, and all sorts of toys. She gets top of the line cat food, purified water, and treats. I also made him a cat door that she can come and go as she pleases, and the cat door is a bit of an issue though, then first she tends to bring dead creatures through the door with him while in the Springtime. There have been squirrels, bunnies, and bird carcasses in my house… Second, other stray cats have thought about coming in the door. Can you imagine the brawl if that happened? The worst is that it isn’t airslender to have a cat door. There are gaps on each side of the swinging flap. I need to let it swing in and out after all. The cat door is actually a homemade insert in my window too. I did the best I could, but frigid air while in the winter and hot air while in the Summer leaks in, however alabama gets quite hot over the summer; Keeping the apartment cool is a full time task. It costs money to pump out that level of AC. The air leaking out due to a cat door actually entirely adds up. I can’t detach it in my cat’s lifetime though. She would go crazy without her own door.

Birmingham Alabama multi split air conditioning