How do I keep my outside cat warm?

Insulate the shelter with straw, not hay. Mylar blankets cut to size can also help cats retain warmth. Avoid using conventional fabric blankets or towels, which absorb moisture and can make the interior cold. Placing the shelter on a pallet or other surface to raise it off the ground can also help to insulate it.

What is the best bedding for an outdoor cat?

Straw

How do you keep a cat house warm in the winter?

Blankets, towels, flat newspapers, etc., retain wetness and should not be used. They absorb body heat and will actually make the cat colder. Straw is a good insulating material to use. Straw is better than hay because it can absorb more moisture and is less prone to mold or rot.