My cat usually has the run of the house at night, except the bedrooms. However, recently she's been getting into the room the baby sleeps in, which needs to stop. I tend to leave the door to that room slightly ajar because the opening and closing of the door wakes the baby up. So I think I need to start shutting the cat in a room at night. We don't have a utility space so the options are the small downstairs toilet where her litter tray currently is and the conservatory. The conservatory is much bigger but is much cooler at night. Do you think either is viable as an option? She's short-haired. There is an igloo bed she could use in the conservatory.