The short answer for degus: indoors
A pet degu is an indoor animal. In the wild, degus live in burrow systems in Chile's dry scrubland, where they retreat underground to escape both midday heat and night cold. A garden enclosure in a temperate climate offers almost the reverse of that: damp air, cold nights, driving rain and long stretches where the temperature swings far more in a day than a degu's body is designed to handle. Indoors, you control that environment, and for degus control is the whole point.
Why outdoor housing works against a degu
Heat is the first problem. Degus cope poorly once a cage sits in direct sun, because they cannot sweat and their thick coat insulates them against the cold they rarely meet as pets, not the heat they do. Cold and damp are the second problem: a wet, chilly degu is vulnerable to respiratory trouble, and wooden outdoor hutches grow mould in their corners that a chewing degu then ingests. The third problem is company they never asked for. Foxes, neighbourhood cats and rats all investigate an outdoor cage, and even when the wire holds, a prey animal that smells a predator every night lives in a state of low-level alarm. Add that degus are escape artists who gnaw relentlessly, and a wooden hutch has a limited lifespan before a determined pair chews an exit.
The indoor setup a degu actually needs
Choose a tall, all-metal cage with narrow bar spacing and several levels, because degus climb, leap and chew for hours a day and plastic bases do not survive them. Site it in a room that stays comfortably warm, out of direct sun and away from radiators and draughty doorways. Degus are sociable and chatty, so a lived-in family room suits them better than a silent spare room, though not right beside a television. Line shelves for their feet, give deep bedding for digging, add a solid running wheel and wooden chew toys, and plan daily time out of the cage in a degu-proofed room so they can burn off their considerable energy. Keep them in a pair or small group of their own kind; a lone degu indoors is a lonely one.
Company matters as much as the cage indoors
Degus are colony animals, and indoor housing only works if the colony comes with them: keep at least a pair, ideally littermates of the same sex or a neutered male with females, because a single degu in a big cage is still a lonely degu. Their chattering, wrestling and shared dust baths are not decoration — they are how degus regulate stress, and an indoor pair will use every level of a tall cage together in a way a lone animal never does.
When to check in with a vet
Housing and health meet quickly in degus. A degu that sits fluffed and quiet in a cage that has been in the sun, or one that sneezes and wheezes after a move to a damper room, needs a vet promptly rather than a watch-and-wait. Likewise, a degu going off food after chewing painted or treated wood from a damaged cage should be seen the same day.
Wherever your degus' cage ends up in the house, KinsLe Family Sharing lets you hand profile access to chosen relatives, so family beyond the person who set the cage up can still open it and put faces to the chattering pair inside.