The atrium domus is what we associate with Roman housing, thanks to the excavations at Pompeii. It developed out of the need for patrons to have somewhere for their clients to wait for them, whilst being suitably impressed by the great patron's grand ancestors. Atrium houses became architecturally redundant in Rome itself once there was an emperor, but continued to be popular in the provinces.
North African architecture to this day is designed to keep out the heat, and this is not a new concept. The Hadrianic houses at Bulla Regia in Tunisia had at atrium carved down into the basement, and sophisticated water features designed to keep the inhabitants of Massinissa's old capital cool in the heat.
The villas survive with lavish decoration. My slides are in storage, but the WMF has some photos.