Cat door allows AC to leak out

I rescued a stray cat off the streets of Birmingham.

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 his own room in the house. I have a queen sized bed with soft sheets for him to sleep on. He has a large cat tree, ledges, scratchers, posts, and all sorts of toys. He gets top of the line cat food, purified water, and treats. I also made him a cat door that he can come and go as he pleases. The cat door is a bit of an issue though. First he tends to bring dead animals through the door with him during 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 airtight 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 cold air during the winter and hot air during the summer leaks in. Alabama gets quite hot over the summer. Keeping the house cool is a full time job. It costs money to pump out that level of AC. The air leaking out due to a cat door probably really adds up. I can’t remove it in my cat’s lifetime though. He would go crazy without his own door.
Birmingham Alabama air conditioning business