Mike S. wrote:

I need to try to insulate a cat house/box just for temporary use...

Cats make heat, and warm air rises. Can you make an entrance below
the house or a platform inside so the cat can sit above the top of
the entrance? A plastic flap hanging over the door would also help.

An ASHRAE-standard normally-active 6.61 pound cat makes 68.02 Btu/h.
Under a 2 ft^2 R1 cardboard roof, it can be 34 F warmer than outdoors.
Add some carpet under or over the roof to make it warmer.

Nick