We built a heated outdoor cat house for our cat and she didn`t help one bit.
It took her almost a week to realize she was supposed to go in it instead of on top of it. 
TA I have to say you're wrong on this, let me explain (I took care of a cat colony for almost 20 years so I learned a thing or two).
The cat didn't go inside because if there is the possibility of an hostile dog nearby it would be fatal.
Before going inside to sleep the cat must be absolutely sure there are no dogs.
I found a couple of times dead cats who find themselves trapped with no way out in a "cat house" like you kindly build.