Insulating a cat house

Hi,

I'm trying to build a cat house and I thought I would calculate the exact thickness of insulating material I would need in order to keep my cat toasty when it gets cold. I'm not sure if I have the right process though. I thought I would ball park how many calories a cat burns in an hour using internet data, convert to watts, and then use the heat flow rate equation: [tex]W = \frac{k_h A \Delta T}{x}[/tex] where W is less power than the cat outputs, A is the area of the box, delta t is the difference between average outside temperature and the temperature of the cat, k is the thermal conductivity constant of the material, and x is the required thickness. One issue I see is that the temperature in the box will rise at a linear/exponential (?) rate rather than be constant, but I'm not sure how to factor that in as I've never done calculus based physics, so is using the temperature of the cat for delta T going to lead to a decent approximation?

Does anyone have any tips for how I can find this information?

Thanks!