The temple and altar served the Imperial cult and were dedicated to Emperor Domitian (AD 81-96); after his death and the condemnation of his memory (damnation memoriae), however, they were dedicated to the Flavian family. The temple, with its 8 x 13 columns constructed upon a six-stepped substructure (24 x 34 m), was erected on a terrace supported by mighty buttresses. After the victory of Christianity it was torn down to its foundations and today is has almost completely disappeared.
The terrain has changed a lot. I found an article stating "For example, the two Doric half-columns, as well as the pilaster figures rebuilt and visible on site today in an architectural trial restoration, were found in the area of the Lower Agora. Their attribution to the façade of the temple terrace occurred merely on the grounds of strong similarities to the architectural ornamentation of other buildings located around the Plaza of Domitian." So they are the most photographed "example"of the former temple, and are probably not even from it.