I have seen and read that a styrofoam cooler with a hole cut out inside a regular cooler with the same hole cut out works great. A blanket inside is perfect. And you can drape a cloth over the hole if you need it.
Coolers (an old one would be perfect), two plastic bins (one inside the other, insulation between the two), etc. - lots of ideas.
I went on Amazon & there are at least 2 insulated houses that I think would work well & purportedly, they are ‘easy’ to assemble. She has a covered front porch where the house would sit so rain/snow are not an issue even if the house is ‘weatherproof’ (one house is for sure).
The cat ... he’s an older orange striped cat, very sweet. My cousin’s daughter lives next door - it’s the country so the house is within sight, not immediately next door. The daughter is a magnet for stray cats - they show up or she finds kittens along the road, etc. This cat was a stray & living outdoors/being fed by the daughter. He visited my cousin’s house next door when her husband B (my actual first cousin) was alive & decided to stay. He got attached to B & became his cat, was allowed in the house. When B died, the cat obviously ‘looked’ for him & missed him. B’s widow has some sentimental attachment to the cat, but is now dealing with the cat by herself - not a problem until she ended up in the hospital for 2 months & now is very frail with mobility issues.
I helped her take the cat to the vet earlier this year before she ended up in the hospital. I had cats for years so I know how to handle them & he obviously likes me, comes running to see me when I show up, even though I put him in the carrier for the vet trip. The daughter asked if I wanted him when her mom was in the hospital, but my mom said no, even to having him strictly outdoors. Our shop garage has a cat door so it would be a good setup, but it’s mom’s house .....
Anyway, I am going to offer to put together a house if she will order it & I will provide the straw. All of the feral cat sites say use straw, no blankets or cat beds - they get damp & straw stays dry, plus the cats can burrow down in it. Straw is good for dog houses, too. Fingers crossed she’ll order a house, otherwise I will just make one & take it over there - I think I have a large, old cooler that leaks water so we don’t use it any more.