I’ve never had a cat that didn’t want to cram themselves down at the far end of their crate at the vet’s office. Once they’ve gotten themselves down there they can get really upset when the vet reaches in to try and remove them. All you need is a nicely sized, thin piece of fabric inside of the crate they can crawl under. Look for a cotton knit fabric. This kind of fabric won’t fray so you can just cut it to size without having to hem the edges. It will also breathe nicely so you don’t have to worry about your cat getting overheated.