This is called the Terrace House. You can see its red roof on some pictures. It is a very ancient construction: The Terrace House was built in the 4th century BC, possibly to serve as a treasury or for storage. Its flat roof was part of the Temple Terrace area. In Hellenistic times, it appears that the roof caved in, since the rooms were filled up with debris, which may have given better stability to this part of the Temple Terrace.

On the map this house must be the unnamed construction to the right of the Andron A.