We have a lean too, which is pretty dry except for a few areas where water drips through the plastic roof. The doors are always open so there is a cross draft. My question is do I go for a indoor cat bed (I'm thinking fabric kennel, or teepee) or an outdoor bed (I just use a enclosed litter tray with a catflap door (a bag stops the draughts getting in through the top vent). The bed would be placed well off the floor either on a chair or on a plastic box. Oh and there is no heating in there.