Asian Garden Dormice require a large habitat furnished with plants, branches and other climbing material. Although mostly arboreal, some Garden Dormice can adapt to more horizontal space so your environment may need to be adapted if your Dormice are less active.
They also like various tunnels, tubes and other shelters and some keepers have reported their Garden Dormice are happier in a more enclosed environment suggesting that a large wooden vivarium may suit better than a vivarium or tank with glass to all four sides. This may be due to the fact that their natural habitats would be tree canopys or rocky outcrops with little open space.
A useful addition to your Asian Garden Dormouse vivarium is a sturdy wooden trellis or similar to give the same climbing opportunities as a wire cage, but without the worries over bumblefoot or interaction with other household pets. Vivariums will need additional ventilation added however.
Like other species of Dormice, Asian Garden Dormice should be kept at a warm room temperature to avoid them entering a state of torpor. A temperature guage can be a useful way of monitoring this.